Daily Papers

It has been difficult to accurately model the physics of the interaction between a robot and the objects it manipulates, including contact mechanics, coupled contact dynamics, deformations, stiffness and friction. We present RoboSimStudio (RSS), an interactive toolkit that makes choices of solver, contact model, and physical parameters explicit and editable, allowing both humans and coding agents to quickly create and iteratively refine simulations based on observed physical behavior. We implement RSS with the open Newton physics simulation system and describe experiments with human-guided real2sim using (1) visual evaluation, (2) force-feedback and (3) agentic Real2Sim2Real. Code, video and additional information can be found on the project website: https://robosimstudio.github.io

While current humanoid whole-body control frameworks predominantly rely on the static environment assumptions, addressing tasks characterized by high dynamism and complex interactions presents a formidable challenge. In this paper, we address humanoid skateboarding, a highly challenging task requiring stable dynamic maneuvering on an underactuated wheeled platform. This integrated system is governed by non-holonomic constraints and tightly coupled human-object interactions. Successfully executing this task requires simultaneous mastery of hybrid contact dynamics and robust balance control on a mechanically coupled, dynamically unstable skateboard. To overcome the aforementioned challenges, we propose HUSKY, a learning-based framework that integrates humanoid-skateboard system modeling and physics-aware whole-body control. We first model the coupling relationship between board tilt and truck steering angles, enabling a principled analysis of system dynamics. Building upon this, HUSKY leverages Adversarial Motion Priors (AMP) to learn human-like pushing motions and employs a physics-guided, heading-oriented strategy for lean-to-steer behaviors. Moreover, a trajectory-guided mechanism ensures smooth and stable transitions between pushing and steering. Experimental results on the Unitree G1 humanoid platform demonstrate that our framework enables stable and agile maneuvering on skateboards in real-world scenarios. The project page is available on https://husky-humanoid.github.io/.

Humanoid foundation models are advancing faster than we can evaluate them. While real-world testing is expensive and difficult to reproduce, existing simulation benchmarks focus primarily on table-top or wheeled robots. A scalable and reproducible benchmark for whole-body humanoid loco-manipulation remains an open problem. To this end, we present SIMPLE, a unified simulation testbed for humanoid policy learning and evaluation. SIMPLE couples the accurate contact-rich dynamics of MuJoCo with the photorealistic rendering of IsaacSim. It provides a large-scale environment comprising 60 diverse whole-body tasks, 50 indoor scenes, and over 1,000 object assets. To facilitate scalable data collection, the framework integrates two data generation pipelines: automated trajectory generation via motion planning and a low-latency VR teleoperation interface. We further integrate and benchmark mainstream humanoid policies at scale in SIMPLE, including lightweight imitation networks, large vision-language-action (VLA) models, and recent world action models (WAMs). Our experiments reveal a strong correlation between policy performance in simulation and the real world. Furthermore, we demonstrate that policies trained on data collected in SIMPLE can be transferred zero-shot to physical humanoid robots under similar settings, providing a robust and reproducible foundation for humanoid robotics research.

Dexterous manipulation depends on contact dynamics that are often only partially observable from vision. Recent World-Action Models (WAMs) couple predictive video world modeling with action generation, but remain largely vision-centric and therefore cannot directly model these contact dynamics. We present DexTacWAM, a visuo-tactile WAM that encodes each fingertip independently, aggregates the resulting features through a finger- and pose-aware tactile compressor, and injects the tactile latent into a video diffusion world model for joint visuo-tactile world modeling. Across six contact-rich dexterous manipulation tasks on a 22-DoF bimanual platform, DexTacWAM achieves the highest score on every task, averaging 70.6 versus 38.0 for the strongest baseline. Ablations attribute the gain to modeling contact evolution as part of the predicted world state rather than tactile conditioning alone: removing tactile world modeling reduces the four-task mean from 74.7 to 26.6 while keeping the same tactile features and action expert. After four hours of tactile-encoder adaptation with a frozen pretrained vision VAE, our continual vision-to-touch learning extends the pretrained video model to touch using roughly 100 demonstrations per task without tactile midtraining, while retaining visual prediction quality within 0.5 dB of vision-only counterparts. The compressor retains 89.4% of pre-fusion contact recall while enabling 2.26x faster training and 1.29x faster inference. Together, these results show that pretrained video priors can be extended to distributed multi-finger contact dynamics in a data- and compute-efficient manner.

Whole-arm manipulation involves direct contact with the environment while the robot completes a task by distributing contact across multiple links as contacts form, slide, and break. This setting breaks common implicit assumptions in many learning-based manipulation pipelines: arm configuration tightly couples motion and contact forces, contact state is partially observed under occlusion, and purely learned rollouts can become physically inconsistent under distribution shift because many multi-link contact configurations are sparsely represented in the data. To address this, we propose TACTIC (Tactile and Vision Conditioned Contact-Centric Control), a receding-horizon controller for whole-arm manipulation. TACTIC uses a contact-centric hybrid predictive model that combines RGB-D, distributed tactile sensing, and a compact 2D proximity representation. The model couples a learned, action-conditioned latent dynamics model with analytical kinematics through contact Jacobians, enabling rollouts of future contact configurations and interaction forces. TACTIC integrates these rollouts into a sampling-based MPC planner with contact-aware action sampling: contact Jacobian-based projections steer sampled action sequences toward force-modulating directions, and objectives defined over predicted proximity and interaction forces trade task progress against whole-arm force regulation. We evaluate TACTIC in simulation against state-of-the-art model-based and model-free methods, and perform ablations that isolate the contribution of each design choice. TACTIC consistently outperforms other methods. We further demonstrate real-world performance on a robot with distributed tactile sensing across three whole-arm manipulation tasks that require multi-contact trajectories: turning over and repositioning a manikin, and goal-reaching in a 3D dynamic maze. Website: https://emprise.cs.cornell.edu/tactic

World models offer a promising avenue for more faithfully capturing complex dynamics, including contacts and non-rigidity, as well as complex sensory information, such as visual perception, in situations where standard simulators struggle. However, these models are computationally complex to evaluate, posing a challenge for popular RL approaches that have been successfully used with simulators to solve complex locomotion tasks but yet struggle with manipulation. This paper introduces a method that bypasses simulators entirely, training RL policies inside world models learned from robots' interactions with real environments. At its core, our approach enables policy training with large-scale diffusion models via a novel decoupled first-order gradient (FoG) method: a full-scale world model generates accurate forward trajectories, while a lightweight latent-space surrogate approximates its local dynamics for efficient gradient computation. This coupling of a local and global world model ensures high-fidelity unrolling alongside computationally tractable differentiation. We demonstrate the efficacy of our method on the Push-T manipulation task, where it significantly outperforms PPO in sample efficiency. We further evaluate our approach through an ego-centric object manipulation task with a quadruped. Together, these results demonstrate that learning inside data-driven world models is a promising pathway for solving hard-to-model RL tasks in image space without reliance on hand-crafted physics simulators.

We address the task of generating physically accurate and visually faithful 4D Human-Object Interaction (HOI). Given a static 3D human and target object represented as 3D Gaussian Splats (3DGS), our goal is to synthesize dynamic scenes where the human actively engages with the object through actions, such as punching or kicking, in accordance with a given input text. To this end, we introduce PhyGenHOI, a novel framework that couples generative human motion with an explicit physical object simulation. We model the human as a semantic agent driven by a Motion Diffusion Model (MDM) and the object as a physical agent simulated via the Material Point Method (MPM), utilizing 3D Gaussians as a unified, differentiable representation. We supervise their interaction through three coupled mechanisms: (1) A Windowed Attraction Loss that temporally synchronizes generative motion to intercept the object; (2) A Contact-Driven Re-simulation step that triggers physically consistent momentum transfer upon impact; and (3) A Masked Video-SDS objective that injects video-based priors to enhance contact fidelity. Experiments show PhyGenHOI generates physically consistent 4D HOI across diverse actions, humans, and objects, outperforming baselines. Project page and videos: https://omerbenishu.github.io/PhyGenHOI/

The true promise of humanoid robotics lies beyond single-agent autonomy: two or more humanoids must engage in physically grounded, socially meaningful whole-body interactions that echo the richness of human social interaction. However, single-humanoid methods suffer from the isolation issue, ignoring inter-agent dynamics and causing misaligned contacts, interpenetrations, and unrealistic motions. To address this, we present Harmanoid , a dual-humanoid motion imitation framework that transfers interacting human motions to two robots while preserving both kinematic fidelity and physical realism. Harmanoid comprises two key components: (i) contact-aware motion retargeting, which restores inter-body coordination by aligning SMPL contacts with robot vertices, and (ii) interaction-driven motion controller, which leverages interaction-specific rewards to enforce coordinated keypoints and physically plausible contacts. By explicitly modeling inter-agent contacts and interaction-aware dynamics, Harmanoid captures the coupled behaviors between humanoids that single-humanoid frameworks inherently overlook. Experiments demonstrate that Harmanoid significantly improves interactive motion imitation, surpassing existing single-humanoid frameworks that largely fail in such scenarios.

Behavioral foundation models (BFMs) have recently shown that a single humanoid policy can support diverse whole-body control, but extending such generality to physical interaction remains challenging. We introduce I-BFM, to our knowledge the first BFM for humanoid-object interaction. Rather than relying on task-specific policies or reference tracking, I-BFM learns a shared representation of the coupled dynamics among the humanoid, objects, and their contacts using forward-backward representations and unsupervised reinforcement learning. Given a downstream task reward, the same policy can be directly conditioned on a latent command to execute closed-loop interaction without task-specific policy optimization. To improve interaction control over different time scales, we further train the policy with both short-horizon interaction targets and longer-horizon goal targets. A single I-BFM policy performs carrying, pushing, and kicking, while also supporting goal reaching, motion tracking, stylistic control, and long-horizon task chaining. More importantly, it remains effective after large deviations from nominal execution: on Carry, I-BFM achieves 94.3% nominal success and retains 89.3% success after robot falls, compared with 1.3% for a planning-based baseline. Real-world experiments on a Unitree G1 further demonstrate diverse loco-manipulation behaviors, rapid recovery from interaction failures and external disturbances, and task chaining without task-specific retraining.

Dexterous interaction with articulated objects is important for household, assistive, and humanoid manipulation, where multi-finger hands can provide compliant contact patterns beyond parallel-jaw grasping. However, articulated-object manipulation differs from static-object manipulation: the target part cannot be directly actuated, and its motion must emerge through sustained physical hand--handle contact. This makes the transition from object-centric articulated generation to hand-driven dexterous hand--object interaction non-trivial, since geometric trajectory replay or open-loop execution does not model the contact dynamics required to move the articulated part. Moreover, policies trained only for task completion under fixed dynamics can overfit nominal contact loads, especially without tactile or force feedback, and may degrade when the contact load changes. To address these challenges, we present DragMesh-2, a contact-driven framework for dexterous interaction with articulated objects that extends articulated interaction from object-centric generation to hand-driven dexterous hand--object interaction, where articulated motion must arise through physical contact. We further propose PICA, a physically informed contact-aware training mechanism that injects physical signals into policy learning without tactile or force feedback, improving robustness and task success under changing contact loads. Finally, we conduct systematic evaluation across multiple damping conditions and articulated-object categories to study robustness under contact-load variation, and provide a pure-geometry dexterous interaction resource to support future loco-manipulation and humanoid hand--object interaction research. Across seven GAPartNet objects, DragMesh-2 achieves stronger robustness under contact-load variation than the compared methods while maintaining high task success across damping conditions.

We investigate solutions to a coupled system of partial differential equations that describe a multilayered filtration system. Namely, we study the interaction of a viscous incompressible flow with bulk poroelasticity, via a poroelastic interface. The configuration consists of two 3D toroidal subdomains connected via a plate interface, which permits elastic deformation and perfusive fluid dynamics. The governing dynamics comprise Stokes equations in the bulk fluid region, Biot's equations in the bulk poroelastic region, and the recent poroplate of Mikelić at the interface. Coupling occurs on the top and lower surfaces of the plate, and involves conservation of mass, stress balance, and a certain slip condition for the fluid free-flow. We seek strong (and mild) solutions in the Hilbert space framework via the Lumer-Phillips theorem. The resolvent analysis employs a nonstandard mixed variational formulation which captures the complex, multi-physics coupling at the interface. We explicitly characterize the infinitesimal generator associated to the linear Cauchy problem and establish the generation of a C_0-semigroup on a suitably chosen finite-energy space. With the semigroup in hand, we may treat elastic nonlinearities for plate displacements through perturbation theory. These result parallel those for Biot-Stokes filtration systems, and complement the recently established weak solution theory for multilayer filtrations. The agency of the semigroup straightforwardly admits structural (plate) nonlinearity into the dynamics. Future stability and regularity analyses for multilayer filtrations are also made possible by these results, as well as a comparison of spectral and regularity properties between filtration configurations, and the elucidation of the mitigating poroplate dynamics as possibly regularizing and stabilizing.

Contact-rich manipulation requires estimating forces, slip and contact geometry that can remain ambiguous in scene images. Optical tactile sensors provide both visual observations of the contact surface and mechanical measurements, yet learning from these signals raises two challenges: representing contact beyond appearance and transferring its benefits to a policy that does not require fingertip observations at deployment. We introduce HapticWAM, a world-action model that combines heterogeneous tactile encoding, structured contact prediction and teacher-student distillation. Its teacher encodes gel images together with deformation, shear, distributed forces, resultant wrench and derived contact state into a frozen video backbone. Rather than predicting tactile pixels alone, the model jointly generates actions and a contact package describing future events and mechanics. Anticipatory Contact Coupling uses the previously imagined package to condition attention, preserving a contact-related input when direct tactile observations are unavailable. Haptic-Imagination Distillation transfers both contact futures and action predictions to a student that retains the generative contact head but removes its fingertip input branches. On a real-world setup, across three contact-rich pick-and-place tasks, HapticWAM Student achieves a 77% per-task mean success rate (41 of 50 starts, 82% pooled), reaching 95% on one of the tasks, outperforming the evaluated teacher and baseline configurations.

Physics simulation for contact-rich robotics is often bottlenecked by contact resolution: mainstream engines enforce non-penetration and Coulomb friction via complementarity constraints or constrained optimization, requiring per-step iterative solves whose cost grows superlinearly with contact density. We present ComFree-Sim, a GPU-parallelized analytical contact physics engine built on complementarity-free contact modeling. ComFree-Sim computes contact impulses in closed form via an impedance-style prediction--correction update in the dual cone of Coulomb friction. Contact computation decouples across contact pairs and becomes separable across cone facets, mapping naturally to GPU kernels and yielding near-linear runtime scaling with the number of contacts. We further extend the formulation to a unified 6D contact model capturing tangential, torsional, and rolling friction, and introduce a practical dual-cone impedance heuristic. ComFree-Sim is implemented in Warp and exposed through a MuJoCo-compatible interface as a drop-in backend alternative to MuJoCo Warp (MJWarp). Experiments benchmark penetration, friction behaviors, stability, and simulation runtime scaling against MJWarp, demonstrating near-linear scaling and 2--3 times higher throughput in dense contact scenes with comparable physical fidelity. We deploy ComFree-Sim in real-time MPC for in-hand dexterous manipulation on a real-world multi-fingered LEAP hand and in dynamics-aware motion retargeting, demonstrating that low-latency simulation yields higher closed-loop success rates and enables practical high-frequency control in contact-rich tasks.

To model high-risk traffic densities a cellular automaton model is constructed, exhibiting Ising model-like properties. The attraction-repulsion forces between vehicles are evaluated as coupling, and the coupling function p(1-p)=g/8, where p is the initial distribution of cells with state 1, and g is the Moore neighbor count, which has roots cos^2(π/8) and sin^2(π/8) for g=1. This is achieved without the use of any trigonometric functions in the code. From the roots, the tangent polynomial tan^2(x) + tan(x) emerges. Kramers-Wannier duality is recovered and it is conjectured that the 1/2 difference between the roots serves as a fixed point for a projection mechanism from the 2-dimensional Ising model onto a 1-dimensional Ising chain through the Gudermannian function. The sigmoid evaluated at the proposed fixed point is substituted into the derivative of the logistic coupling function, σ(1/2)(1-σ(1/2)), yielding a numerical approximation to the three-dimensional Ising inverse critical coupling. Finally, the results are linked to risk densities in traffic and vehicle types, accounting for the amplification of fatal accidents.

Daily activities require humans to coordinate whole-body motion with the motion of surrounding objects. Despite recent progress in human-object interaction (HOI) generation, most existing methods assume interactions with a single rigid object and do not extend well to scenarios involving a variable number of objects or articulated objects with diverse joint mechanisms. We propose surface keypoint trajectories as an object motion representation: for each rigid component, whether a standalone object or one part of an articulated assembly, we track a small set of non-collinear surface points over time. This representation handles multi-object coordination and diverse articulation mechanisms directly from point dynamics without requiring explicit joint-type specification. To model when and where each body region contacts each object, we introduce a spatio-temporal contact distance field that extends distance-based contact modeling to whole-body, multi-object, and articulated settings. We factorize HOI generation into three stages: generating object motions from text or waypoints, predicting the contact distance field, and synthesizing whole-body motion with contact-guided optimization. Experiments on ParaHome, HIMO, ARCTIC, and OMOMO demonstrate better or comparable performance to existing methods across single-object, multi-object, and articulated interaction settings.

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-your-own coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.

Text- and image-conditioned video generation models have achieved strong visual fidelity and temporal coherence, but they often fail to generate motion governed by kinematic and geometric constraints. In these settings, object parts must remain rigid, maintain contact or coupling with neighboring components, and transfer motion consistently across connected parts. These requirements are especially explicit in articulated mechanical assemblies, where motion is constrained by rigid-link geometry, contact/coupling relations, and transmission through kinematic chains. A generated video may therefore appear plausible while violating the intended mechanism, such as rotating a part that should translate, deforming a rigid component, breaking coupling between parts, or failing to move downstream components. To evaluate this gap, We introduce MechVerse, a benchmark for mechanically consistent image-to-video generation. MechVerse contains 21,156 synthetic clips from 1,357 mechanical assemblies across 141 categories, organized into three tiers of increasing kinematic complexity: independent articulation, pairwise coupling, and densely coupled multi-part mechanisms. Each clip is paired with a structured prompt describing part identities, stationary supports, moving components, motion primitives, direction, speed/extent, and inter-part dependencies. We evaluate proprietary, open-source, and fine-tuned image-to-video models using standard video metrics, instruction-following scores, and human judgments of motion correctness and kinematic coupling. Results show that current models can preserve appearance and smoothness while failing to generate mechanically admissible motion, with errors increasing as coupling complexity grows. MechVerse provides a benchmark for measuring and improving mechanism-aware video generation from image and language inputs.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

Modifications to test-time sampling have emerged as an important extension to diffusion algorithms, with the goal of biasing the generative process to achieve a given objective without having to retrain the entire diffusion model. However, generating jointly correlated samples from multiple pre-trained diffusion models while simultaneously enforcing task-specific constraints without costly retraining has remained challenging. To this end, we propose Projected Coupled Diffusion (PCD), a novel test-time framework for constrained joint generation. PCD introduces a coupled guidance term into the generative dynamics to encourage coordination between diffusion models and incorporates a projection step at each diffusion step to enforce hard constraints. Empirically, we demonstrate the effectiveness of PCD in application scenarios of image-pair generation, object manipulation, and multi-robot motion planning. Our results show improved coupling effects and guaranteed constraint satisfaction without incurring excessive computational costs.

The Milky Way is known to contain a stellar bar, as are a significant fraction of disc galaxies across the universe. Our understanding of bar evolution, both theoretically and through analysis of simulations indicates that bars both grow in amplitude and slow down over time through interaction and angular momentum exchange with the galaxy's dark matter halo. Understanding the physical mechanisms underlying this coupling requires modelling of the structural deformations to the potential that are mutually induced between components. In this work we use Basis Function Expansion (BFE) in combination with multichannel Singular Spectral Analysis (mSSA) as a non-parametric analysis tool to illustrate the coupling between the bar and the dark halo in a single high-resolution isolated barred disc galaxy simulation. We demonstrate the power of mSSA to extract and quantify explicitly coupled dynamical modes, determining growth rates, pattern speeds and phase lags for different stages of evolution of the stellar bar and the dark matter response. BFE & mSSA together grant us the ability to explore the importance and physical mechanisms of bar-halo coupling, and other dynamically coupled structures across a wide range of dynamical environments.

Hand-Object Interaction (HOI) generation plays a critical role in advancing applications across animation and robotics. Current video-based methods are predominantly single-view, which impedes comprehensive 3D geometry perception and often results in geometric distortions or unrealistic motion patterns. While 3D HOI approaches can generate dynamically plausible motions, their dependence on high-quality 3D data captured in controlled laboratory settings severely limits their generalization to real-world scenarios. To overcome these limitations, we introduce SyncMV4D, the first model that jointly generates synchronized multi-view HOI videos and 4D motions by unifying visual prior, motion dynamics, and multi-view geometry. Our framework features two core innovations: (1) a Multi-view Joint Diffusion (MJD) model that co-generates HOI videos and intermediate motions, and (2) a Diffusion Points Aligner (DPA) that refines the coarse intermediate motion into globally aligned 4D metric point tracks. To tightly couple 2D appearance with 4D dynamics, we establish a closed-loop, mutually enhancing cycle. During the diffusion denoising process, the generated video conditions the refinement of the 4D motion, while the aligned 4D point tracks are reprojected to guide next-step joint generation. Experimentally, our method demonstrates superior performance to state-of-the-art alternatives in visual realism, motion plausibility, and multi-view consistency.

Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach to solve physics-based initial value problems using unsupervised machine learning. We propose a deep learning framework that models the dynamics of a variety of mechanical systems through neural networks. Our framework is flexible, allowing us to solve non-linear, coupled, and chaotic dynamical systems. We demonstrate the effectiveness of our approach on systems including a free particle, a particle in a gravitational field, a classical pendulum, and the H\'enon--Heiles system (a pair of coupled harmonic oscillators with a non-linear perturbation, used in celestial mechanics). Our results show that deep neural networks can successfully approximate solutions to these problems, producing trajectories which conserve physical properties such as energy and those with stationary action. We note that probabilistic activation functions, as defined in this paper, are required to learn any solutions of initial value problems in their strictest sense, and we introduce coupled neural networks to learn solutions of coupled systems.

We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form rough domain boundaries, which defines collision interfaces in time and space. We show that statistical properties of such interfaces depend on the kinetics of the growing interfaces before collision, but are independent of the details of their interaction and of their fluctuations during the collision. Those properties exhibit dynamic scaling with exponents related to the growth kinetics, but their distributions may be non-universal. These results are supported by simulations of lattice models with irreversible dynamics and local interactions. Relations to first passage processes are discussed and a possible application to grain boundary formation in two-dimensional materials is suggested.

A cumulative variational framework for solid deformation is proposed. Its central organizing principle is the recursive combination of three structural components of one material body: a compatible Cosserat component, a distributed-incompatibility component, and a defect-source component. At any prescribed external condition these components constitute a combined material state. They are governed under common physical boundary and initial conditions and are coupled through one cumulative energy and the associated field equations. They are not separate boundary-value problems and need not appear in a prescribed temporal sequence. The cumulative character of the framework concerns the response of the combined state to variation of externally prescribed conditions. For the special case of an initially perfect body, loss of stability may produce successive branches with defect and then source participation. Such a sequence is a bifurcation property of the selected initial state and constitutive energy, rather than a defining hierarchy of the framework. A one-dimensional specialization illustrates structural bifurcation, residual deformation and residual stress produced by retained structure, dependence on the initial combined state, directional memory under reverse loading, parametric cumulative hysteresis, and changes of observable tangent stiffness associated with structural stabilization. A spatial extension introduces defect and source gradient terms and yields a size-dependent structural stability operator. For the stable quartic energy considered, the gradient terms regularize nonuniform perturbations but do not by themselves generate a finite-wavelength localization instability on an already stable three-component branch. The examples thereby distinguish consequences of the cumulative structure and energy from phenomena requiring additional constitutive evolution laws.

Wheel-legged robots with integrated manipulators hold great promise for mobile manipulation in logistics, industrial automation, and human-robot collaboration. However, unified control of such systems remains challenging due to the redundancy in degrees of freedom, complex wheel-ground contact dynamics, and the need for seamless coordination between locomotion and manipulation. In this work, we present the design and whole-body motion control of an omnidirectional wheel-legged quadrupedal robot equipped with a dexterous manipulator. The proposed platform incorporates independently actuated steering modules and hub-driven wheels, enabling agile omnidirectional locomotion with high maneuverability in structured environments. To address the challenges of contact-rich interaction, we develop a contact-aware whole-body dynamic optimization framework that integrates point-contact modeling for manipulation with line-contact modeling for wheel-ground interactions. A warm-start strategy is introduced to accelerate online optimization, ensuring real-time feasibility for high-dimensional control. Furthermore, a unified kinematic model tailored for the robot's 4WIS-4WID actuation scheme eliminates the need for mode switching across different locomotion strategies, improving control consistency and robustness. Simulation and experimental results validate the effectiveness of the proposed framework, demonstrating agile terrain traversal, high-speed omnidirectional mobility, and precise manipulation under diverse scenarios, underscoring the system's potential for factory automation, urban logistics, and service robotics in semi-structured environments.

Scientific applications increasingly demand real-time surrogate models that can capture the behavior of strongly coupled multiphysics systems driven by multiple input functions, such as in thermo-mechanical and electro-thermal processes. While neural operator frameworks, such as Deep Operator Networks (DeepONets), have shown considerable success in single-physics settings, their extension to multiphysics problems remains poorly understood. In particular, the challenge of learning nonlinear interactions between tightly coupled physical fields has received little systematic attention. This study addresses a foundational question: should the architectural design of a neural operator reflect the strength of physical coupling it aims to model? To answer this, we present the first comprehensive, architecture-aware evaluation of DeepONet variants across three regimes: single-physics, weakly coupled, and strongly coupled multiphysics systems. We consider a reaction-diffusion equation with dual spatial inputs, a nonlinear thermo-electrical problem with bidirectional coupling through temperature-dependent conductivity, and a viscoplastic thermo-mechanical model of steel solidification governed by transient phase-driven interactions. Two operator-learning frameworks, the classical DeepONet and its sequential GRU-based extension, S-DeepONet, are benchmarked using both single-branch and multi-branch (MIONet-style) architectures. Our results demonstrate that architectural alignment with physical coupling is crucial: single-branch networks significantly outperform multi-branch counterparts in strongly coupled settings, whereas multi-branch encodings offer advantages for decoupled or single-physics problems. Once trained, these surrogates achieve full-field predictions up to 1.8e4 times faster than high-fidelity finite-element solvers, without compromising solution accuracy.

Expert demonstrations show how to complete contact-rich tasks, but provide limited coverage of how interaction forces respond to different actions. Task-agnostic play provides broader experience of contact dynamics without specifying task goals. To fully leverage these two types of data, we introduce ForceWAM, a force world action model that decouples knowledge of task-compatible interaction outcomes from knowledge of how local actions change contact. A world model learns from successful demonstrations to jointly predict future video and six-axis force/torque trajectories. Together, these futures describe the expected evolution of motion and contact during the task. A separate inverse dynamics model (IDM) learns from both task and play, mapping current observations and recorded visual-wrench futures to their associated robot actions. Play data thus provide knowledge of force responses for goal-directed execution. At deployment, the IDM reactively translates generated futures into actions, reusing them with fresh wrench feedback between world-model updates. Across real-robot force-regulated sliding, box flipping with and without disturbances, and ring placement, ForceWAM achieves 85-95% mean success, surpassing world-modeling and reactive baselines. Our experiments further show that adding task-agnostic play data improves success by 15-45 percentage points, demonstrating its value for learning contact-rich execution. Project page and code are available at https://force-wam.github.io/.

Modeling the hand-object (HO) interaction not only requires estimation of the HO pose, but also pays attention to the contact due to their interaction. Significant progress has been made in estimating hand and object separately with deep learning methods, simultaneous HO pose estimation and contact modeling has not yet been fully explored. In this paper, we present an explicit contact representation namely Contact Potential Field (CPF), and a learning-fitting hybrid framework namely MIHO to Modeling the Interaction of Hand and Object. In CPF, we treat each contacting HO vertex pair as a spring-mass system. Hence the whole system forms a potential field with minimal elastic energy at the grasp position. Extensive experiments on the two commonly used benchmarks have demonstrated that our method can achieve state-of-the-art in several reconstruction metrics, and allow us to produce more physically plausible HO pose even when the ground-truth exhibits severe interpenetration or disjointedness. Our code is available at https://github.com/lixiny/CPF.

The relationship between balance laws and the Principle of Virtual Work as well as the structure of contact interactions in continua remain foundational issues in Mechanics. In this work, we revisit these issues within the distributional framework emphasized by Paul Germain. We show that while the Principle of Virtual Work implies balance of forces and moments for nth-gradient continua, balance laws alone do not suffice to characterize equilibrium for n geq 2. We then reexamine Noll's classical theorem asserting that surface contact forces depend solely on the unit normal to the surface and identify the precise role of his additional assumptions, namely the absence of edge and wedge contact interactions and the boundedness of the surface contact density on the space of oriented surfaces. We demonstrate that these hypotheses fail for general higher-gradient continua. Consequently, the presence of curvature-dependent surface contact forces in such materials does not conflict with Noll's theorem and refutes his claim of their nonexistence.

Contact-rich policies often fail because distinct physical states look alike yet require different actions. Cameras may not reveal whether a connector is aligned or fully seated, while many normal-only tactile sensors can miss the tangential interactions perpendicular to the grasping direction that distinguish these states. We ask whether a learning policy needs calibrated shear measurements, or only a repeatable observation that separates shear-dependent contact states. We introduce TacGooseBumps (TacGB), a passive domed film that mechanically encodes tangential loading as pattern changes in an existing sensor's pressure map. Tangential loading tilts each dome and redistributes pressure across its footprint; an end-to-end policy consumes the resulting maps without added electronics, force reconstruction, or taxel-level dome alignment. Across four imitation-learning tasks and two data-collection pipelines, TacGB improves goal attainment, efficiency, and contact quality: insertion success increases by up to 36 percentage points, and successful insertions are completed faster, while fragile-object placement becomes gentler and drawing becomes more continuous and straight. Signal, stage-wise, failure-mode, and trajectory analyses link these gains to contact regimes in which task-relevant tangential interactions are poorly resolved by vision and normal pressure alone. Together, these results show that shear need not be measured metrically to benefit robot learning; it can instead be mechanically encoded without changing the underlying tactile sensor or the policy's pressure-map input format.

Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-Parisi-Zhang (KPZ) universality class. This has been established for phase oscillators and also for some limit-cycle oscillators, both in the presence of columnar (quenched) disorder and of time-dependent noise, by extensive numerical simulations, and has been analytically motivated by continuum approximations in the strong oscillator coupling limit. The robustness and the precise boundaries in parameter space for such critical behavior remain unclear, however, which may preclude further developments, including the extension of these results to higher dimensions and the experimental observation of nonequilibrium criticality in synchronizing (e.g.~electronic or chemical) oscillators. We here present complete numerical phase diagrams of one-dimensional synchronization, including saturation times and values, but, most importantly, also dynamical features giving insight into the gradual emergence of synchronous dynamics, based on systems of phase oscillators with either type of randomness. In the absence of synchronization, the dynamics evolves as expected for random deposition (for time-dependent noise) or linear growth (for columnar disorder), while a crossover from Edwards-Wilkinson to Kardar-Parisi-Zhang behavior (with the corresponding type of randomness) is observed as the randomness strength, or the nonoddity of the coupling among oscillators, is increased in the synchronous region -- their combined effect being partially captured by the so-called KPZ coupling. The distortion of scaling due to phase slips near the desynchronization boundary, a feature that is likely to play a role in experimental contexts, is also discussed.

Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering disciplines. Most real-world physical systems across various disciplines are actually involved in multiple coupled physical fields rather than a single field. However, previous machine learning studies mainly focused on solving single-field problems, but overlooked the importance and characteristics of multiphysics problems in real world. Multiphysics PDEs typically entail multiple strongly coupled variables, thereby introducing additional complexity and challenges, such as inter-field coupling. Both benchmarking and solving multiphysics problems with machine learning remain largely unexamined. To identify and address the emerging challenges in multiphysics problems, we mainly made three contributions in this work. First, we collect the first general multiphysics dataset, the Multiphysics Bench, that focuses on multiphysics PDE solving with machine learning. Multiphysics Bench is also the most comprehensive PDE dataset to date, featuring the broadest range of coupling types, the greatest diversity of PDE formulations, and the largest dataset scale. Second, we conduct the first systematic investigation on multiple representative learning-based PDE solvers, such as PINNs, FNO, DeepONet, and DiffusionPDE solvers, on multiphysics problems. Unfortunately, naively applying these existing solvers usually show very poor performance for solving multiphysics. Third, through extensive experiments and discussions, we report multiple insights and a bag of useful tricks for solving multiphysics with machine learning, motivating future directions in the study and simulation of complex, coupled physical systems.

Recent video generation research has focused heavily on isolated actions, leaving interactive motions-such as hand-face interactions-largely unexamined. These interactions are essential for emerging biometric authentication systems, which rely on interactive motion-based anti-spoofing approaches. From a security perspective, there is a growing need for large-scale, high-quality interactive videos to train and strengthen authentication models. In this work, we introduce a novel paradigm for animating realistic hand-face interactions. Our approach simultaneously learns spatio-temporal contact dynamics and biomechanically plausible deformation effects, enabling natural interactions where hand movements induce anatomically accurate facial deformations while maintaining collision-free contact. To facilitate this research, we present InterHF, a large-scale hand-face interaction dataset featuring 18 interaction patterns and 90,000 annotated videos. Additionally, we propose InterAnimate, a region-aware diffusion model designed specifically for interaction animation. InterAnimate leverages learnable spatial and temporal latents to effectively capture dynamic interaction priors and integrates a region-aware interaction mechanism that injects these priors into the denoising process. To the best of our knowledge, this work represents the first large-scale effort to systematically study human hand-face interactions. Qualitative and quantitative results show InterAnimate produces highly realistic animations, setting a new benchmark. Code and data will be made public to advance research.

We introduce multi-task Visuo-Tactile World Models (VT-WM), which capture the physics of contact through touch reasoning. By complementing vision with tactile sensing, VT-WM better understands robot-object interactions in contact-rich tasks, avoiding common failure modes of vision-only models under occlusion or ambiguous contact states, such as objects disappearing, teleporting, or moving in ways that violate basic physics. Trained across a set of contact-rich manipulation tasks, VT-WM improves physical fidelity in imagination, achieving 33% better performance at maintaining object permanence and 29% better compliance with the laws of motion in autoregressive rollouts. Moreover, experiments show that grounding in contact dynamics also translates to planning. In zero-shot real-robot experiments, VT-WM achieves up to 35% higher success rates, with the largest gains in multi-step, contact-rich tasks. Finally, VT-WM demonstrates significant downstream versatility, effectively adapting its learned contact dynamics to a novel task and achieving reliable planning success with only a limited set of demonstrations.

This paper tackles the problem of physics-aware human motion synthesis in a dynamic scene. Unlike existing works which mainly tend to generate physically unrealistic motions due to limited contact modeling, typically restricted to hands, in this paper, we introduce a physics-aware human motion generation framework that explicitly models the full spectrum of human-related forces, including human-object, human-scene, and internal body dynamics.~Our method imposes soft physical constraints to maintain force and torque balance, ensuring physically grounded motion synthesis. We further propose a novel continuous distance-based force model that generalizes contact modeling to arbitrary surfaces, capturing interactions not only with static environments but also with dynamic, moving objects. Extensive experiments show that our approach significantly improves physical plausibility and generalizes well to complex scenes, setting a new benchmark for physically consistent human motion generation.

We present DecoupledGaussian, a novel system that decouples static objects from their contacted surfaces captured in-the-wild videos, a key prerequisite for realistic Newtonian-based physical simulations. Unlike prior methods focused on synthetic data or elastic jittering along the contact surface, which prevent objects from fully detaching or moving independently, DecoupledGaussian allows for significant positional changes without being constrained by the initial contacted surface. Recognizing the limitations of current 2D inpainting tools for restoring 3D locations, our approach proposes joint Poisson fields to repair and expand the Gaussians of both objects and contacted scenes after separation. This is complemented by a multi-carve strategy to refine the object's geometry. Our system enables realistic simulations of decoupling motions, collisions, and fractures driven by user-specified impulses, supporting complex interactions within and across multiple scenes. We validate DecoupledGaussian through a comprehensive user study and quantitative benchmarks. This system enhances digital interaction with objects and scenes in real-world environments, benefiting industries such as VR, robotics, and autonomous driving. Our project page is at: https://wangmiaowei.github.io/DecoupledGaussian.github.io/.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

This paper investigates the stability of steady transonic shocks with constant states in rectangular nozzles under small three dimensional perturbations of the external force and the exit pressure. Mathematically, the problem can be formulated as a nonlinear free boundary problem for a hyperbolic-elliptic coupled PDE system. One of the key difficulties lies in the arbitrary location of the background shock, which may lead to multiple shock solutions for the same external force and exit pressure under perturbations, revealing the instability of the background shock. We reformulate the steady Euler equations in terms of deformation and vorticity to effectively decompose the hyperbolic and elliptic modes. Linearizing the reformulated system and the Rankine-Hugoniot conditions at background transonic shocks, we find that the class of nonzero horizontal external forces helps to uniquely determine the shock location, where the conservation of mass plays a critical role. A delicate iteration is developed to establish the existence and structural stability of transonic shock solutions. Our analysis shows that the stability mechanisms of steady transonic shocks in flat and divergent nozzles are quite different in many aspects.

This paper addresses a novel task of anticipating 3D human-object interactions (HOIs). Most existing research on HOI synthesis lacks comprehensive whole-body interactions with dynamic objects, e.g., often limited to manipulating small or static objects. Our task is significantly more challenging, as it requires modeling dynamic objects with various shapes, capturing whole-body motion, and ensuring physically valid interactions. To this end, we propose InterDiff, a framework comprising two key steps: (i) interaction diffusion, where we leverage a diffusion model to encode the distribution of future human-object interactions; (ii) interaction correction, where we introduce a physics-informed predictor to correct denoised HOIs in a diffusion step. Our key insight is to inject prior knowledge that the interactions under reference with respect to contact points follow a simple pattern and are easily predictable. Experiments on multiple human-object interaction datasets demonstrate the effectiveness of our method for this task, capable of producing realistic, vivid, and remarkably long-term 3D HOI predictions.

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular interactions through integral terms and drug-induced cell death. The model accounts for spatial heterogeneity in both tumor cell density and drug concentration while capturing the complex dynamics of drug resistance development. We first establish the well-posedness of the coupled system by proving the existence and uniqueness of a solution under appropriate regularity conditions. The optimal control problem is then formulated to minimize tumor size while accounting for drug toxicity constraints. Using variational methods, we derive the necessary optimality conditions and characterize the optimal control through an adjoint system. Theoretical results can help to design effective chemotherapy schedules that balance treatment efficacy with adverse effects.

The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the atmosphere-ocean coupling. Thus, the proposed method should be viewed as potentially applicable to air-sea coupled flows in turbulent regime. The method consists of two key ingredients. The geometric averaging approach is used for efficient and stable decoupling of the problem, which would allow for the usage of preexisting codes for the air and sea domain separately, as "black boxes". This is combined with the variational multiscale stabilization technique for treating flows at high Reynolds numbers. We prove the stability and accuracy of the method and provide several numerical tests to assess both the quantitative and qualitative features of the computed solution.

Accurate physical simulation is crucial for the development and validation of control algorithms in robotic systems. Recent works in Reinforcement Learning (RL) take notably advantage of extensive simulations to produce efficient robot control. State-of-the-art servo actuator models generally fail at capturing the complex friction dynamics of these systems. This limits the transferability of simulated behaviors to real-world applications. In this work, we present extended friction models that allow to more accurately simulate servo actuator dynamics. We propose a comprehensive analysis of various friction models, present a method for identifying model parameters using recorded trajectories from a pendulum test bench, and demonstrate how these models can be integrated into physics engines. The proposed friction models are validated on four distinct servo actuators and tested on 2R manipulators, showing significant improvements in accuracy over the standard Coulomb-Viscous model. Our results highlight the importance of considering advanced friction effects in the simulation of servo actuators to enhance the realism and reliability of robotic simulations.

Contact-rich manipulation tasks with stiff frictional elements like connector insertion are difficult to model with rigid-body simulators. In this work, we propose a new approach for modeling these environments by learning a quasi-static contact force model instead of a full simulator. Using a feature vector that contains information about the configuration and control, we find a linear mapping adequately captures the relationship between this feature vector and the sensed contact forces. A novel Linear Model Learning (LML) algorithm is used to solve for the globally optimal mapping in real time without any matrix inversions, resulting in an algorithm that runs in nearly constant time on a GPU as the model size increases. We validate the proposed approach for connector insertion both in simulation and hardware experiments, where the learned model is combined with an optimization-based controller to achieve smooth insertions in the presence of misalignments and uncertainty. Our website featuring videos, code, and more materials is available at https://model-based-plugging.github.io/.

Contact-rich manipulation requires policies to react to local deformation, pressure, slip, and friction, yet these cues are temporally sparse and often invisible in visual observations. Existing visual-tactile policies usually feed tactile observations directly into action prediction, but rarely model tactile deformation dynamics during action generation. In this paper, we introduce VT-WAM, a Visual-Tactile World Action Model that jointly learns future visual prediction, tactile deformation prediction, and action prediction within a unified flow matching framework. In particular, VT-WAM introduces (1) Asymmetric Mixture-of-Transformers (MoT) attention to bridge a first-frame visual anchor with temporal tactile dynamics, and (2) contact-gated Action-Visual-Tactile Attention Guidance (AVTAG) to encourage action queries to rely on tactile evidence during contact phases. Across six real-world contact-rich manipulation tasks, VT-WAM achieves a 71.67% average success rate, outperforming Fast-WAM by 26.67% and OmniVTLA by 35.84%. Ablations demonstrate that modeling tactile deformation dynamics and guiding contact-phase tactile attention are both important for contact-rich tasks. Project website: https://vt-wam.github.io/.

Generalized reaction-diffusion systems encompass diverse transport mechanisms and coupled reaction kinetics. A central question for neural PDE solvers is what should be learned so that a common interface can accommodate phase-field and degenerate transport, local reactions, and multispecies coupling. We propose the Neural Constitutive Laws--Mass-Compression-Transport (NCL-MCT) Solver, which learns PDE-specific constitutive responses while retaining temporal evolution in a shared MCT integrator. Transport is represented through mobility and thermodynamic driving force, and reaction through relative reaction rates. These constitutive responses depend on the current density rather than explicitly on the initial condition or elapsed time, motivating their reuse across different initial conditions and time horizons. The same interface supports velocity-data supervision and known-law supervision, neither of which requires time integration during training. When constitutive laws are known, supervision can be evaluated on independently sampled density fields, enabling trajectory-free constitutive learning without generating solution trajectories. Across seven systems, separately trained constitutive modules share the same interface and MCT integrator and achieve relative rollout L^2 errors of 10^{-4} to 10^{-2}. Tests with unseen initial-condition families and an extended time horizon assess reuse beyond training conditions, while separate experiments demonstrate trajectory-free constitutive learning. These results support constitutive responses as an effective learning target for a shared neural PDE framework.

We present a novel paradigm for modeling certain types of dynamic simulation in real-time with the aid of neural networks. In order to significantly reduce the requirements on data (especially time-dependent data), as well as decrease generalization error, our approach utilizes a data-driven neural network only to capture quasistatic information (instead of dynamic or time-dependent information). Subsequently, we augment our quasistatic neural network (QNN) inference with a (real-time) dynamic simulation layer. Our key insight is that the dynamic modes lost when using a QNN approximation can be captured with a quite simple (and decoupled) zero-restlength spring model, which can be integrated analytically (as opposed to numerically) and thus has no time-step stability restrictions. Additionally, we demonstrate that the spring constitutive parameters can be robustly learned from a surprisingly small amount of dynamic simulation data. Although we illustrate the efficacy of our approach by considering soft-tissue dynamics on animated human bodies, the paradigm is extensible to many different simulation frameworks.

Ensuring safety is of paramount importance in physical human-robot interaction applications. This requires both adherence to safety constraints defined on the system state, as well as guaranteeing compliant behavior of the robot. If the underlying dynamical system is known exactly, the former can be addressed with the help of control barrier functions. The incorporation of elastic actuators in the robot's mechanical design can address the latter requirement. However, this elasticity can increase the complexity of the resulting system, leading to unmodeled dynamics, such that control barrier functions cannot directly ensure safety. In this paper, we mitigate this issue by learning the unknown dynamics using Gaussian process regression. By employing the model in a feedback linearizing control law, the safety conditions resulting from control barrier functions can be robustified to take into account model errors, while remaining feasible. In order to enforce them on-line, we formulate the derived safety conditions in the form of a second-order cone program. We demonstrate our proposed approach with simulations on a two-degree-of-freedom planar robot with elastic joints.

Operating robots precisely and at high speeds has been a long-standing goal of robotics research. Balancing these competing demands is key to enabling the seamless collaboration of robots and humans and increasing task performance. However, traditional motor-driven systems often fall short in this balancing act. Due to their rigid and often heavy design exacerbated by positioning the motors into the joints, faster motions of such robots transfer high forces at impact. To enable precise and safe dynamic motions, we introduce a four degree-of-freedom~(DoF) tendon-driven robot arm. Tendons allow placing the actuation at the base to reduce the robot's inertia, which we show significantly reduces peak collision forces compared to conventional robots with motors placed near the joints. Pairing our robot with pneumatic muscles allows generating high forces and highly accelerated motions, while benefiting from impact resilience through passive compliance. Since tendons are subject to additional friction and hence prone to wear and tear, we validate the reliability of our robotic arm on various experiments, including long-term dynamic motions. We also demonstrate its ease of control by quantifying the nonlinearities of the system and the performance on a challenging dynamic table tennis task learned from scratch using reinforcement learning. We open-source the entire hardware design, which can be largely 3D printed, the control software, and a proprioceptive dataset of 25 days of diverse robot motions at webdav.tuebingen.mpg.de/pamy2.

We study the dynamics of an inextensible, closed interface subject to bending forces and immersed in a two-dimensional and incompressible Stokes fluid. We formulate the problem as a boundary integral equation in terms of the tangent angle and demonstrate the well-posedness in suitable time-weighted spaces of the resulting nonlinear and nonlocal system. The solution is furthermore shown to be smooth for positive times. Numerical computations are performed to initiate the study of the long-time behavior of the interface.

Dexterous manipulation with contact-rich interactions is crucial for advanced robotics. While recent diffusion-based planning approaches show promise for simple manipulation tasks, they often produce unrealistic ghost states (e.g., the object automatically moves without hand contact) or lack adaptability when handling complex sequential interactions. In this work, we introduce DexHandDiff, an interaction-aware diffusion planning framework for adaptive dexterous manipulation. DexHandDiff models joint state-action dynamics through a dual-phase diffusion process which consists of pre-interaction contact alignment and post-contact goal-directed control, enabling goal-adaptive generalizable dexterous manipulation. Additionally, we incorporate dynamics model-based dual guidance and leverage large language models for automated guidance function generation, enhancing generalizability for physical interactions and facilitating diverse goal adaptation through language cues. Experiments on physical interaction tasks such as door opening, pen and block re-orientation, object relocation, and hammer striking demonstrate DexHandDiff's effectiveness on goals outside training distributions, achieving over twice the average success rate (59.2% vs. 29.5%) compared to existing methods. Our framework achieves an average of 70.7% success rate on goal adaptive dexterous tasks, highlighting its robustness and flexibility in contact-rich manipulation.

Humans are highly adaptable, swiftly switching between different modes to progressively handle different tasks, situations and contexts. In Human-object interaction (HOI) activities, these modes can be attributed to two mechanisms: (1) the large-scale consistent plan for the whole activity and (2) the small-scale children interactive actions that start and end along the timeline. While neuroscience and cognitive science have confirmed this multi-mechanism nature of human behavior, machine modeling approaches for human motion are trailing behind. While attempted to use gradually morphing structures (e.g., graph attention networks) to model the dynamic HOI patterns, they miss the expeditious and discrete mode-switching nature of the human motion. To bridge that gap, this work proposes to model two concurrent mechanisms that jointly control human motion: the Persistent process that runs continually on the global scale, and the Transient sub-processes that operate intermittently on the local context of the human while interacting with objects. These two mechanisms form an interactive Persistent-Transient Duality that synergistically governs the activity sequences. We model this conceptual duality by a parent-child neural network of Persistent and Transient channels with a dedicated neural module for dynamic mechanism switching. The framework is trialed on HOI motion forecasting. On two rich datasets and a wide variety of settings, the model consistently delivers superior performances, proving its suitability for the challenge.

We present Dojo, a differentiable physics engine for robotics that prioritizes stable simulation, accurate contact physics, and differentiability with respect to states, actions, and system parameters. Dojo models hard contact and friction with a nonlinear complementarity problem with second-order cone constraints. We introduce a custom primal-dual interior-point method to solve the second order cone program for stable forward simulation over a broad range of sample rates. We obtain smooth gradient approximations with this solver through the implicit function theorem, giving gradients that are useful for downstream trajectory optimization, policy optimization, and system identification applications. Specifically, we propose to use the central path parameter threshold in the interior point solver as a user-tunable design parameter. A high value gives a smooth approximation to contact dynamics with smooth gradients for optimization and learning, while a low value gives precise simulation rollouts with hard contact. We demonstrate Dojo's differentiability in trajectory optimization, policy learning, and system identification examples. We also benchmark Dojo against MuJoCo, PyBullet, Drake, and Brax on a variety of robot models, and study the stability and simulation quality over a range of sample frequencies and accuracy tolerances. Finally, we evaluate the sim-to-real gap in hardware experiments with a Ufactory xArm 6 robot. Dojo is an open source project implemented in Julia with Python bindings, with code available at https://github.com/dojo-sim/Dojo.jl.

While large-scale human motion capture datasets have advanced human motion generation, modeling and generating dynamic 3D human-object interactions (HOIs) remain challenging due to dataset limitations. Existing datasets often lack extensive, high-quality motion and annotation and exhibit artifacts such as contact penetration, floating, and incorrect hand motions. To address these issues, we introduce InterAct, a large-scale 3D HOI benchmark featuring dataset and methodological advancements. First, we consolidate and standardize 21.81 hours of HOI data from diverse sources, enriching it with detailed textual annotations. Second, we propose a unified optimization framework to enhance data quality by reducing artifacts and correcting hand motions. Leveraging the principle of contact invariance, we maintain human-object relationships while introducing motion variations, expanding the dataset to 30.70 hours. Third, we define six benchmarking tasks and develop a unified HOI generative modeling perspective, achieving state-of-the-art performance. Extensive experiments validate the utility of our dataset as a foundational resource for advancing 3D human-object interaction generation. To support continued research in this area, the dataset is publicly available at https://github.com/wzyabcas/InterAct, and will be actively maintained.

Modeling spatiotemporal coupling is a key challenge in building physical intelligence across scales, from microscopic to macroscopic. Existing models capture such structure broadly through physics-motivated dynamical formulations or learning-motivated architectures. The former provide stronger priors but may constrain flexibility, whereas the latter are more flexible but leave the spatiotemporal coupling largely implicit. We therefore seek an approach that combines flexible learning with an explicit geometric bias for jointly modeling time and space. To this end, we propose Minkowski Positional Encoding (MinkowskiPE), which uses joint temporal and spatial coordinates to parameterize Lorentz transformations applied to query and key features. With MinkowskiPE, the query-key attention score depends on position only through the relative spacetime displacement between the two tokens and is therefore invariant to global translation of the coordinates. This paradigm retains the standard dot-product attention interface and remains compatible with efficient attention implementations. We evaluate MinkowskiPE on microscopic molecular dynamics and macroscopic video prediction tasks, achieving the best results on all nine multi-trajectory molecular evaluations and reducing KTH video-prediction MSE by 9.9% relative to the best baseline while using roughly one-tenth as many parameters.

Simulating trajectories of multi-particle systems on complex energy landscapes is a central task in molecular dynamics (MD) and drug discovery, but remains challenging at scale due to computationally expensive and long simulations. Previous approaches leverage techniques such as flow or Schrödinger bridge matching to implicitly learn joint trajectories through data snapshots. However, many systems, including biomolecular systems and heterogeneous cell populations, undergo dynamic interactions that evolve over their trajectory and cannot be captured through static snapshots. To close this gap, we introduce Entangled Schrödinger Bridge Matching (EntangledSBM), a framework that learns the first- and second-order stochastic dynamics of interacting, multi-particle systems where the direction and magnitude of each particle's path depend dynamically on the paths of the other particles. We define the Entangled Schrödinger Bridge (EntangledSB) problem as solving a coupled system of bias forces that entangle particle velocities. We show that our framework accurately simulates heterogeneous cell populations under perturbations and rare transitions in high-dimensional biomolecular systems.

Hypothesis: Bacterial contamination of surfaces poses a major threat to public health. Designing effective antibacterial or self-cleaning surfaces requires understanding how bacteria-laden droplets interact with solid substrates and how readily they can be removed. We hypothesize that bacterial motility critically influences the early-stage surface interaction (i.e., surface adhesion) of bacteria-laden droplets, which cannot be captured by conventional contact angle goniometry. Experiments: Sessile droplets containing live and dead Escherichia coli (E. coli) were studied to probe their wetting and interfacial behavior. Contact angle goniometry was used to probe dynamic wetting, while a cantilever-deflection-based method was used to quantify adhesion. Internal flow dynamics were visualized using micro-particle image velocimetry (PIV) and analyzed statistically. Complementary sliding experiments on moderately wettable substrates were performed to assess contact line mobility under tilt. Findings: Despite lower surface tension, droplets containing live bacteria exhibited lower surface adhesion forces than their dead counterparts, with adhesion further decreasing at higher bacterial concentrations. Micro-PIV revealed that flagellated live E. coli actively resist evaporation-driven capillary flow via upstream migration, while at higher concentrations, collective dynamics emerge, producing spatially coherent bacterial motion despite temporal variability. These coordinated flows disrupt passive transport and promote depinning of the contact line, thereby reducing adhesion. Sliding experiments confirmed enhanced contact line mobility and frequent stick-slip motion in live droplets, even with lower receding contact angles and higher hysteresis. These findings provide mechanistic insight into droplet retention, informing the design of self-cleaning/antifouling surfaces.

Biological tissues exhibit complex behaviors with their dynamics often resembling inert soft matter such as liquids, polymers, colloids, and liquid crystals. These analogies enable physics-based approaches for investigations of emergent behaviors in biological processes. A well-studied case is the spreading of cellular aggregates on solid surfaces, where they display dynamics similar to viscous droplets. In vivo, however, cells and tissues are in a confined environment with varying geometries and mechanical properties to which they need to adapt. In this work, we compressed cellular aggregates between two solid surfaces and studied their dynamics using microscopy, and computer simulations. The confined cellular aggregates transitioned from compressed spheres into dynamic living capillary bridges exhibiting bridge thinning and a convex-to-concave meniscus curvature transition. We found that the stability of the bridge is determined by the interplay between cell growth and cell spreading on the confining surfaces. This interaction leads to bridge rupture at a critical length scale determined by the distance between the plates. The force distributions, formation and stability regimes of the living capillary bridges were characterized with full 3D computer simulations that included cell division, migration and growth dynamics, directly showing how mechanical principles govern the behavior of the living bridges; cellular aggregates display jamming and stiffening analogously to granular matter, and cell division along the long axis enhances thinning. Based on our results, we propose a new class of active soft matter behavior, where cellular aggregates exhibit liquid-like adaptation to confinement, but with self-organized rupturing driven by biological activity.

Synthesizing realistic human-object interaction motions is a critical problem in VR/AR and human animation. Unlike the commonly studied scenarios involving a single human or hand interacting with one object, we address a more generic multi-body setting with arbitrary numbers of humans, hands, and objects. This complexity introduces significant challenges in synchronizing motions due to the high correlations and mutual influences among bodies. To address these challenges, we introduce SyncDiff, a novel method for multi-body interaction synthesis using a synchronized motion diffusion strategy. SyncDiff employs a single diffusion model to capture the joint distribution of multi-body motions. To enhance motion fidelity, we propose a frequency-domain motion decomposition scheme. Additionally, we introduce a new set of alignment scores to emphasize the synchronization of different body motions. SyncDiff jointly optimizes both data sample likelihood and alignment likelihood through an explicit synchronization strategy. Extensive experiments across four datasets with various multi-body configurations demonstrate the superiority of SyncDiff over existing state-of-the-art motion synthesis methods.

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is considered. For general functional forms of the nonlinear prey birthrate/prey deathrate or reaction terms, a Hopf bifurcation is shown to occur at two different critical values of the traveling wave speed. The post-bifurcation dynamics is investigated for five different functional forms of the nonlinearities. In cases where the bifurcation is supercritical, the post-bifurcation behaviour yields stable periodic orbits of the traveling-wave ODEs in the spatial variable. These correspond to stable periodic wavetrains of the full PDEs. Subcritical Hopf bifurcations yield more complex post-bifurcation dynamics in the PDE wavetrains. In special cases where the subcritical bifurcation marks the end of the regime of stability, the post-bifurcation behavior in the spatial ODEs is chaotic, corresponding to wavetrains of the original PDEs which are spatially coherent, but have chaotic temporal dynamics. All the models are integrated numerically to investigate the post-bifurcation dynamics and chaotic regimes are characterized by computing power spectra, autocorrelation functions, and fractal dimensions.

Vision-Language-Action (VLA) models have shown remarkable generalization by mapping web-scale knowledge to robotic control, yet they remain blind to physical contact. Consequently, they struggle with contact-rich manipulation tasks that require reasoning about force, texture, and slip. While some approaches incorporate low-dimensional tactile signals, they fail to capture the high-resolution dynamics essential for such interactions. To address this limitation, we introduce DreamTacVLA, a framework that grounds VLA models in contact physics by learning to feel the future. Our model adopts a hierarchical perception scheme in which high-resolution tactile images serve as micro-vision inputs coupled with wrist-camera local vision and third-person macro vision. To reconcile these multi-scale sensory streams, we first train a unified policy with a Hierarchical Spatial Alignment (HSA) loss that aligns tactile tokens with their spatial counterparts in the wrist and third-person views. To further deepen the model's understanding of fine-grained contact dynamics, we finetune the system with a tactile world model that predicts future tactile signals. To mitigate tactile data scarcity and the wear-prone nature of tactile sensors, we construct a hybrid large-scale dataset sourced from both high-fidelity digital twin and real-world experiments. By anticipating upcoming tactile states, DreamTacVLA acquires a rich model of contact physics and conditions its actions on both real observations and imagined consequences. Across contact-rich manipulation tasks, it outperforms state-of-the-art VLA baselines, achieving up to 95% success, highlighting the importance of understanding physical contact for robust, touch-aware robotic agents.

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

Sampling-based algorithms are viewed as practical solutions for high-dimensional motion planning. Recent progress has taken advantage of random geometric graph theory to show how asymptotic optimality can also be achieved with these methods. Achieving this desirable property for systems with dynamics requires solving a two-point boundary value problem (BVP) in the state space of the underlying dynamical system. It is difficult, however, if not impractical, to generate a BVP solver for a variety of important dynamical models of robots or physically simulated ones. Thus, an open challenge was whether it was even possible to achieve optimality guarantees when planning for systems without access to a BVP solver. This work resolves the above question and describes how to achieve asymptotic optimality for kinodynamic planning using incremental sampling-based planners by introducing a new rigorous framework. Two new methods, Stable Sparse-RRT (SST) and SST*, result from this analysis, which are asymptotically near-optimal and optimal, respectively. The techniques are shown to converge fast to high-quality paths, while they maintain only a sparse set of samples, which makes them computationally efficient. The good performance of the planners is confirmed by experimental results using dynamical systems benchmarks, as well as physically simulated robots.

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the future state distant in time with high accuracy. Although these methods have diverse designs in modeling the coordinates and interacting forces of the system, we show that they actually share a common paradigm that learns the integration of the velocity over the interval between the initial and terminal coordinates. However, their integrand is constant w.r.t. time. Inspired by this observation, we propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas and prove its effectiveness theoretically. Extensive experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.

Human-level contact-rich manipulation relies on the distinct roles of two key modalities: vision provides spatially rich but temporally slow global context, while force sensing captures rapid, high-frequency local contact dynamics. Integrating these signals is challenging due to their fundamental frequency and informational disparities. In this work, we propose ImplicitRDP, a unified end-to-end visual-force diffusion policy that integrates visual planning and reactive force control within a single network. We introduce Structural Slow-Fast Learning, a mechanism utilizing causal attention to simultaneously process asynchronous visual and force tokens, allowing the policy to perform closed-loop adjustments at the force frequency while maintaining the temporal coherence of action chunks. Furthermore, to mitigate modality collapse where end-to-end models fail to adjust the weights across different modalities, we propose Virtual-target-based Representation Regularization. This auxiliary objective maps force feedback into the same space as the action, providing a stronger, physics-grounded learning signal than raw force prediction. Extensive experiments on contact-rich tasks demonstrate that ImplicitRDP significantly outperforms both vision-only and hierarchical baselines, achieving superior reactivity and success rates with a streamlined training pipeline. Code and videos will be publicly available at https://implicit-rdp.github.io.

In parallel simulation, convergence and parallelism are often seen as inherently conflicting objectives. Improved parallelism typically entails lighter local computation and weaker coupling, which unavoidably slow the global convergence. This paper presents a novel GPU algorithm that achieves convergence rates comparable to fullspace Newton's method while maintaining good parallelizability just like the Jacobi method. Our approach is built on a key insight into the phenomenon of overshoot. Overshoot occurs when a local solver aggressively minimizes its local energy without accounting for the global context, resulting in a local update that undermines global convergence. To address this, we derive a theoretically second-order optimal solution to mitigate overshoot. Furthermore, we adapt this solution into a pre-computable form. Leveraging Cubature sampling, our runtime cost is only marginally higher than the Jacobi method, yet our algorithm converges nearly quadratically as Newton's method. We also introduce a novel full-coordinate formulation for more efficient pre-computation. Our method integrates seamlessly with the incremental potential contact method and achieves second-order convergence for both stiff and soft materials. Experimental results demonstrate that our approach delivers high-quality simulations and outperforms state-of-the-art GPU methods with 50 to 100 times better convergence.

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.

Touch contact and pressure are essential for understanding how humans interact with and manipulate objects, insights which can significantly benefit applications in mixed reality and robotics. However, estimating these interactions from an egocentric camera perspective is challenging, largely due to the lack of comprehensive datasets that provide both accurate hand poses on contacting surfaces and detailed annotations of pressure information. In this paper, we introduce EgoPressure, a novel egocentric dataset that captures detailed touch contact and pressure interactions. EgoPressure provides high-resolution pressure intensity annotations for each contact point and includes accurate hand pose meshes obtained through our proposed multi-view, sequence-based optimization method processing data from an 8-camera capture rig. Our dataset comprises 5 hours of recorded interactions from 21 participants captured simultaneously by one head-mounted and seven stationary Kinect cameras, which acquire RGB images and depth maps at 30 Hz. To support future research and benchmarking, we present several baseline models for estimating applied pressure on external surfaces from RGB images, with and without hand pose information. We further explore the joint estimation of the hand mesh and applied pressure. Our experiments demonstrate that pressure and hand pose are complementary for understanding hand-object interactions. ng of hand-object interactions in AR/VR and robotics research. Project page: https://yiming-zhao.github.io/EgoPressure/.

We investigate diffusion approximations for a class of multivariate inhomogeneous finite-velocity random motions motivated by models of active particles. A particle alternates cyclically among prescribed velocity fields V_1,dots,V_p with random run times and evolves according to either a flight dynamics, consisting of piecewise-linear motion, or a gliding dynamics, in which the particle follows the corresponding velocity flow. Under a Kac-type scaling that couples vanishing run times with diverging particle speed, we prove weak convergence of both processes to multidimensional diffusions. It turns out that the order of successive cyclic motions affects the diffusion limit. In addition to the second-order term generated by fluctuations of the random run times, the limiting drift contains directional derivatives DV_i[V_j] of the underlying vector fields. In Stratonovich form, part of this drift is expressed through their Lie brackets [V_i,V_j]. Thus, the generic non-commutativity of the microscopic motions survives the diffusive scaling and generates a macroscopic drift which depends on the cyclic order. The limiting drift also distinguishes the flight and gliding dynamics, despite their being driven by the same vector fields and run times. Several examples, including run-and-reverse motion and cyclic dynamics generated by multiple vector fields, illustrate how the cyclic switching protocol and the geometry of the underlying velocity fields shape the limiting diffusions.

Learning an effective policy to control high-dimensional, overactuated systems is a significant challenge for deep reinforcement learning algorithms. Such control scenarios are often observed in the neural control of vertebrate musculoskeletal systems. The study of these control mechanisms will provide insights into the control of high-dimensional, overactuated systems. The coordination of actuators, known as muscle synergies in neuromechanics, is considered a presumptive mechanism that simplifies the generation of motor commands. The dynamical structure of a system is the basis of its function, allowing us to derive a synergistic representation of actuators. Motivated by this theory, we propose the Dynamical Synergistic Representation (DynSyn) algorithm. DynSyn aims to generate synergistic representations from dynamical structures and perform task-specific, state-dependent adaptation to the representations to improve motor control. We demonstrate DynSyn's efficiency across various tasks involving different musculoskeletal models, achieving state-of-the-art sample efficiency and robustness compared to baseline algorithms. DynSyn generates interpretable synergistic representations that capture the essential features of dynamical structures and demonstrates generalizability across diverse motor tasks.

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. We provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto-Sivashinsky equation in the chaotic regime, and the Navier-Stokes equations in the turbulent regime. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.

We study a dynamical optimal transport problem on path-space with kinetic cost and nonlocal interaction. For a Gaussian interaction kernel, cyclical monotonicity and the regularity of the effective endpoint cost yield a conservative vector field associated with the initial momentum of the optimal trajectories. Separately, the Gaussian interaction potential W_{π_0} satisfies a uniform gradient estimate and, under a quantitative condition on the interaction strength, is a classical and hence viscosity subsolution of an eikonal equation. We also derive the Euler--Lagrange dynamics directly from path-space optimality by means of endpoint-preserving perturbations of the optimal path measure. The associated phase-space marginals satisfy a measure-valued Liouville-type, or nonlocal kinetic, equation driven by the smooth Gaussian self-consistent force. Conversely, a superposition principle lifts suitable measure-valued solutions of the phase-space continuity equation to measures on phase-space trajectories. Thus path-space optimal transport provides a variational connection between endpoint geometry, eikonal behavior of the Gaussian interaction potential, and kinetic mean-field dynamics.

Real-world contact-rich manipulation demands robots to perceive temporal tactile feedback, capture subtle surface deformations, and reason about object properties as well as force dynamics. Although optical tactile sensors are uniquely capable of providing such rich information, existing tactile datasets and models remain limited. These resources primarily focus on object-level attributes (e.g., material) while largely overlooking fine-grained tactile temporal dynamics during physical interactions. We consider that advancing dynamic tactile perception requires a systematic hierarchy of dynamic perception capabilities to guide both data collection and model design. To address the lack of tactile data with rich dynamic information, we present ToucHD, a large-scale hierarchical tactile dataset spanning tactile atomic actions, real-world manipulations, and touch-force paired data. Beyond scale, ToucHD establishes a comprehensive tactile dynamic data ecosystem that explicitly supports hierarchical perception capabilities from the data perspective. Building on it, we propose AnyTouch 2, a general tactile representation learning framework for diverse optical tactile sensors that unifies object-level understanding with fine-grained, force-aware dynamic perception. The framework captures both pixel-level and action-specific deformations across frames, while explicitly modeling physical force dynamics, thereby learning multi-level dynamic perception capabilities from the model perspective. We evaluate our model on benchmarks that covers static object properties and dynamic physical attributes, as well as real-world manipulation tasks spanning multiple tiers of dynamic perception capabilities-from basic object-level understanding to force-aware dexterous manipulation. Experimental results demonstrate consistent and strong performance across sensors and tasks.

It is well-known that inverse dynamics models can improve tracking performance in robot control. These models need to precisely capture the robot dynamics, which consist of well-understood components, e.g., rigid body dynamics, and effects that remain challenging to capture, e.g., stick-slip friction and mechanical flexibilities. Such effects exhibit hysteresis and partial observability, rendering them, particularly challenging to model. Hence, hybrid models, which combine a physical prior with data-driven approaches are especially well-suited in this setting. We present a novel hybrid model formulation that enables us to identify fully physically consistent inertial parameters of a rigid body dynamics model which is paired with a recurrent neural network architecture, allowing us to capture unmodeled partially observable effects using the network memory. We compare our approach against state-of-the-art inverse dynamics models on a 7 degree of freedom manipulator. Using data sets obtained through an optimal experiment design approach, we study the accuracy of offline torque prediction and generalization capabilities of joint learning methods. In control experiments on the real system, we evaluate the model as a feed-forward term for impedance control and show the feedback gains can be drastically reduced to achieve a given tracking accuracy.

Transferring human motion to humanoid robots requires adapting the demonstrated motion to the robot morphology while preserving interactions with the environment. This is particularly challenging for loco-manipulation tasks, where contacts with the ground and manipulated objects must remain consistent despite differences in body proportions. Yet, skeletal motion alone does not fully describe these interactions, and fixing object trajectories limits the adaptation to a new embodiment. In this paper, we introduce OTR ETARGET, a unified approach to jointly retarget robot and multi-object motion from human demonstrations. Our approach represents surface interactions through signed distances, closest surface points, and relative directions, and uses entropic optimal transport to transfer these quantities across human, robot, and object geometries. We incorporate the resulting interaction targets into a constrained inverse kinematics formulation that balances contact preservation with motion style and jointly optimizes robot and object poses at each frame. This formulation accommodates robot-object and object-object interactions without rescaling the scene or the demonstration. We validate the proposed approach on OMOMO, where it achieves a robot- object interaction Jaccard score of 87% and a depth error of 8.7 mm, compared with 28% and 29.3 mm for OmniRetarget. Finally, we demonstrate transfer to a physical G1 humanoid using whole-body policies trained with reinforcement learning on the retargeted references, across motions including two-handed box pick-and-place onto a table.

A primary challenge in using neural networks to approximate nonlinear dynamical systems governed by partial differential equations (PDEs) is transforming these systems into a suitable format, especially when dealing with non-linearizable dynamics or the need for infinite-dimensional spaces for linearization. This paper introduces DyMixOp, a novel neural operator framework for PDEs that integrates insights from complex dynamical systems to address this challenge. Grounded in inertial manifold theory, DyMixOp transforms infinite-dimensional nonlinear PDE dynamics into a finite-dimensional latent space, establishing a structured foundation that maintains essential nonlinear interactions and enhances physical interpretability. A key innovation is the Local-Global-Mixing (LGM) transformation, inspired by convection dynamics in turbulence. This transformation effectively captures both fine-scale details and nonlinear interactions, while mitigating spectral bias commonly found in existing neural operators. The framework is further strengthened by a dynamics-informed architecture that connects multiple LGM layers to approximate linear and nonlinear dynamics, reflecting the temporal evolution of dynamical systems. Experimental results across diverse PDE benchmarks demonstrate that DyMixOp achieves state-of-the-art performance, significantly reducing prediction errors, particularly in convection-dominated scenarios reaching up to 86.7\%, while maintaining computational efficiency and scalability.

I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented by a one-parameter family of operators, evolving on its own time scale. I formalize stratified state spaces capturing multiple levels of synchronized behavior, define an asynchronous evolution metric that quantifies phase-offset distances between subsystems, and characterize emergent coherent topologies arising when subsystems synchronize. Within this framework, I develop formal operators for the evolution of each subsystem and give precise conditions under which phase-aligned synchronization occurs across the lattice. The main results include: (1) the existence and uniqueness of coherent (synchronized) states under a contractive coupling condition, (2) stability of these coherent states and criteria for their emergence as a collective phase transition in a continuous operator topology, and (3) the influence of symmetries, with group-invariant coupling leading to flow-invariant synchrony subspaces and structured cluster dynamics. Proofs are given for each theorem, demonstrating full mathematical rigor. In a final section, I discuss hypothetical applications of this framework to symbolic lattice systems (e.g. subshifts), to invariant group actions on dynamical lattices, and to operator fields over stratified manifolds in the spirit of noncommutative geometry. Throughout, I write in the first person to emphasize the exploratory nature of this work. The paper avoids any reference to cosmology or observers, focusing instead on clean, formal mathematics suitable for a broad array of dynamical systems.

Human-Object Interaction (HOI) is vital for advancing simulation, animation, and robotics, enabling the generation of long-term, physically plausible motions in 3D environments. However, existing methods often fall short of achieving physics realism and supporting diverse types of interactions. To address these challenges, this paper introduces a unified Human-Object Interaction framework that provides unified control over interactions with static scenes and dynamic objects using language commands. The interactions between human and object parts can always be described as the continuous stable Relative Movement Dynamics (RMD) between human and object parts. By leveraging the world knowledge and scene perception capabilities of Vision-Language Models (VLMs), we translate language commands into RMD diagrams, which are used to guide goal-conditioned reinforcement learning for sequential interaction with objects. Our framework supports long-horizon interactions among dynamic, articulated, and static objects. To support the training and evaluation of our framework, we present a new dataset named Interplay, which includes multi-round task plans generated by VLMs, covering both static and dynamic HOI tasks. Extensive experiments demonstrate that our proposed framework can effectively handle a wide range of HOI tasks, showcasing its ability to maintain long-term, multi-round transitions. For more details, please refer to our project webpage: https://rmd-hoi.github.io/.

Contact-rich bimanual manipulation involves precise coordination of two arms to change object states through strategically selected contacts and motions. Due to the inherent complexity of these tasks, acquiring sufficient demonstration data and training policies that generalize to unseen scenarios remain a largely unresolved challenge. Building on recent advances in planning through contacts, we introduce Generalizable Planning-Guided Diffusion Policy Learning (GLIDE), an approach that effectively learns to solve contact-rich bimanual manipulation tasks by leveraging model-based motion planners to generate demonstration data in high-fidelity physics simulation. Through efficient planning in randomized environments, our approach generates large-scale and high-quality synthetic motion trajectories for tasks involving diverse objects and transformations. We then train a task-conditioned diffusion policy via behavior cloning using these demonstrations. To tackle the sim-to-real gap, we propose a set of essential design options in feature extraction, task representation, action prediction, and data augmentation that enable learning robust prediction of smooth action sequences and generalization to unseen scenarios. Through experiments in both simulation and the real world, we demonstrate that our approach can enable a bimanual robotic system to effectively manipulate objects of diverse geometries, dimensions, and physical properties. Website: https://glide-manip.github.io/

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

Contact-rich manipulation requires not only vision-dominant task semantics but also closed-loop reactions to force/torque (F/T) transients. Yet, generative visuomotor policies are typically constrained to low-frequency updates due to inference latency and action chunking, underutilizing F/T for control-rate feedback. Furthermore, existing force-aware methods often inject force continuously and indiscriminately, lacking an explicit mechanism to schedule when / how much / where to apply force across different task phases. We propose PhaForce, a phase-scheduled visual--force policy that coordinates low-rate chunk-level planning and high-rate residual correction via a unified contact/phase schedule. PhaForce comprises (i) a contact-aware phase predictor (CAP) that estimates contact probability and phase belief, (ii) a Slow diffusion planner that performs dual-gated visual--force fusion with orthogonal residual injection to preserve vision semantics while conditioning on force, and (iii) a Fast corrector that applies control-rate phase-routed residuals in interpretable corrective subspaces for within-chunk micro-adjustments. Across multiple real-robot contact-rich tasks, PhaForce achieves an average success rate of 86% (+40 pp over baselines), while also substantially improving contact quality by regulating interaction forces and exhibiting robust adaptability to OOD geometric shifts.

This study introduces amangkurat, an open-source Python library designed for the robust numerical simulation of relativistic scalar field dynamics governed by the nonlinear Klein-Gordon equation in (1+1)D spacetime. The software implements a hybrid computational strategy that couples Fourier pseudo-spectral spatial discretization with a symplectic Størmer-Verlet temporal integrator, ensuring both exponential spatial convergence for smooth solutions and long-term preservation of Hamiltonian structure. To optimize performance, the solver incorporates adaptive timestepping based on Courant-Friedrichs-Lewy (CFL) stability criteria and utilizes Just-In-Time (JIT) compilation for parallelized force computation. The library's capabilities are validated across four canonical physical regimes: dispersive linear wave propagation, static topological kink preservation in phi-fourth theory, integrable breather dynamics in the sine-Gordon model, and non-integrable kink-antikink collisions. Beyond standard numerical validation, this work establishes a multi-faceted analysis framework employing information-theoretic entropy metrics (Shannon, Rényi, and Tsallis), kernel density estimation, and phase space reconstruction to quantify the distinct phenomenological signatures of these regimes. Statistical hypothesis testing confirms that these scenarios represent statistically distinguishable dynamical populations. Benchmarks on standard workstation hardware demonstrate that the implementation achieves high computational efficiency, making it a viable platform for exploratory research and education in nonlinear field theory.

A droplet impacting a deep fluid bath is as common as rain over the ocean. If the impact is sufficiently gentle, the mediating air layer remains intact, and the droplet may rebound completely from the interface. In this work, we experimentally investigate the role of translational bath motion on the bouncing to coalescence transition. Over a range of parameters, we find that the relative bath motion systematically decreases the normal Weber number required to transition from bouncing to merging. Direct numerical simulations demonstrate that the depression created during impact combined with the translational motion of the bath enhances the air layer drainage on the upstream side of the droplet, ultimately favoring coalescence. A simple geometric argument is presented that rationalizes the collapse of the experimental threshold data, extending what is known for the case of axisymmetric normal impacts to the more general 3D scenario of interest herein.

Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the characteristics of the solution fields and their time-dependent dynamics. Although high-fidelity numerical solvers generate the training datasets, they have thus far been excluded from the training process, causing the learned latent dynamics to drift away from the discretized governing physics. This mismatch often limits generalization and forecasting capabilities. In this work, we propose Physics-informed ROM (Φ-ROM) by incorporating differentiable PDE solvers into the training procedure. Specifically, the latent space dynamics and its dependence on PDE parameters are shaped directly by the governing physics encoded in the solver, ensuring a strong correspondence between the full and reduced systems. Our model outperforms state-of-the-art data-driven ROMs and other physics-informed strategies by accurately generalizing to new dynamics arising from unseen parameters, enabling long-term forecasting beyond the training horizon, maintaining continuity in both time and space, and reducing the data cost. Furthermore, Φ-ROM learns to recover and forecast the solution fields even when trained or evaluated with sparse and irregular observations of the fields, providing a flexible framework for field reconstruction and data assimilation. We demonstrate the framework's robustness across various PDE solvers and highlight its broad applicability by providing an open-source JAX implementation that is readily extensible to other PDE systems and differentiable solvers, available at https://phi-rom.github.io.

Handheld data collection systems, such as the Universal Manipulation Interface (UMI), enable scalable data collection across diverse environments but only capture observed actions rather than the desired actions executed by a robot controller. In contrast, teleoperation captures desired actions directly, but is prohibitively time-consuming to collect. We revisit this trade-off through the lens of action validity across task phases. We observe that handheld trajectories provide valid supervision in tolerant, free-space phases, but lack dynamic feasibility in contact-sensitive phases, where tracking observed trajectories at high stiffness produces large, unsafe contact forces. We study the interaction between these two supervision types for contact-rich manipulation and find that training policies that combine handheld data with a small number of targeted teleoperated demonstrations provide an efficient hybrid strategy. Specifically, rather than teleoperating the entire task, we only collect partial teleoperated demonstrations for task segments where base handheld policies fail. However, naively mixing handheld and teleoperated phase-specific data yields worse performance than training on handheld data alone. To address this mismatch between observed and desired supervision, we propose Bi-modal Routing for Imitation Data via Gated Experts (BRIDGE), a mixture of diffusion policy experts that routes between specialist task phase heads conditioned on the current robot state. Notably, our approach enables task-phase specific use of desired actions during contact sensitive segments and improves success rates over handheld-only baselines by up to 36.7% across three contact-rich manipulation tasks.

Accurate aerodynamic modeling of satellites in very low Earth orbit (VLEO) requires gas-surface interaction (GSI) models that capture the full velocity spectrum from thermal to orbital speeds. Atmospheric particles initially strike spacecraft surfaces at hypersonic velocities of 6 000 - 10 000 m/s. Due to surface roughness and complex geometries, especially within air-breathing electric propulsion (ABEP) intake systems, multiple collisions occur, progressively reducing the particle velocities. A recent machine learning framework for deriving scattering kernels from molecular dynamics (MD) simulations has shown promise, but remains limited to high-velocity single impacts and possibly violates fundamental equilibrium principles such as detailed balance. This work extends this machine learning based scattering kernel to cover the complete velocity range using conditional normalizing flows trained with physics-informed constraints, enabling accurate modeling of multi-bounce scenarios in realistic VLEO applications. We train a conditional Real-valued Non-Volume Preserving (cRealNVP) model on expanded molecular dynamics simulations covering velocities from thermal to hypersonic speeds, incorporating a detailed balance loss term. The resulting model demonstrates improved accuracy compared to previous approaches even in the original high-velocity regime, while successfully capturing thermal-velocity scattering. Quantitative assessment shows that thermalization is approximated within acceptable tolerances. This framework provides essential capabilities for accurate ABEP intake optimization and VLEO mission planning while offering a general methodology applicable to broader rarefied gas dynamics problems requiring thermodynamic consistency.

Rich contact perception is crucial for robotic manipulation, yet traditional tactile skins remain expensive and complex to integrate. This paper presents a scalable alternative: high-accuracy whole-body touch localization via vibro-acoustic sensing. By equipping a robotic hand with seven low-cost piezoelectric microphones and leveraging an Audio Spectrogram Transformer, we decode the vibrational signatures generated during physical interaction. Extensive evaluation across stationary and dynamic tasks reveals a localization error of under 5 mm in static conditions. Furthermore, our analysis highlights the distinct influence of material properties: stiff materials (e.g., metal) excel in impulse response localization due to sharp, high-bandwidth responses, whereas textured materials (e.g., wood) provide superior friction-based features for trajectory tracking. The system demonstrates robustness to the robot's own motion, maintaining effective tracking even during active operation. Our primary contribution is demonstrating that complex physical contact dynamics can be effectively decoded from simple vibrational signals, offering a viable pathway to widespread, affordable contact perception in robotics. To accelerate research, we provide our full datasets, models, and experimental setups as open-source resources.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

Molecular dynamics (MD) provides insights into atomic-scale processes by integrating over time the equations that describe the motion of atoms under the action of interatomic forces. Machine learning models have substantially accelerated MD by providing inexpensive predictions of the forces, but they remain constrained to minuscule time integration steps, which are required by the fast time scale of atomic motion. In this work, we propose FlashMD, a method to predict the evolution of positions and momenta over strides that are between one and two orders of magnitude longer than typical MD time steps. We incorporate considerations on the mathematical and physical properties of Hamiltonian dynamics in the architecture, generalize the approach to allow the simulation of any thermodynamic ensemble, and carefully assess the possible failure modes of such a long-stride MD approach. We validate FlashMD's accuracy in reproducing equilibrium and time-dependent properties, using both system-specific and general-purpose models, extending the ability of MD simulation to reach the long time scales needed to model microscopic processes of high scientific and technological relevance.

Ecological interactions are often mediated by feedbacks between organisms and their resource environments. Yet, how resource supply dynamics dictate collective dynamical phases of an ecosystem remains unclear. Here, we analyse a generalised consumer--resource model with non-reciprocal interactions to demonstrate that self-renewing versus externally-supplied resources yield fundamentally different dynamical phase diagrams. As interactions become increasingly non-reciprocal, ecosystems relying on self-renewing resources transition from stable dynamics to chaos and ultimately to infeasibility. By contrast, ecosystems with externally-supplied resources remain stable over a broader parameter range and transition to infeasibility without experiencing an intervening chaotic phase. Using the cavity method, we derive a unified stability condition applicable to a broad class of resource supply functions, explaining why externally-supplied resources can expand the stable region. We show that stability hinges crucially on the susceptibility of resources to perturbations, which depends strongly on their supply. Further, we show that external resource supply suppresses chaos in the unstable region by drastically reducing the susceptibility of resources closest to extinction. Our findings demonstrate that resource dynamics fundamentally reshape the accessible dynamical behaviours of an ecosystem, with implications for interpreting microbial community experiments.

We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis >96) in stable states. Information-theoretic metrics show 10.7% reduction in activator-inhibitor coupling during turbulence versus 6.5% in stable regimes. The solver handles stiffness ratios >6:1 with features including automated equilibrium classification and checkpointing. Effect sizes (delta=0.37--0.78) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics.

Learning to simulate complex physical systems from data has emerged as a promising way to overcome the limitations of traditional numerical solvers, which often require prohibitive computational costs for high-fidelity solutions. Recent Graph Neural Simulators (GNSs) accelerate simulations by learning dynamics on graph-structured data, yet often struggle to capture long-range interactions and suffer from error accumulation under autoregressive rollouts. To address these challenges, we propose Information-preserving Graph Neural Simulators (IGNS), a graph-based neural simulator built on the principles of Hamiltonian dynamics. This structure guarantees preservation of information across the graph, while extending to port-Hamiltonian systems allows the model to capture a broader class of dynamics, including non-conservative effects. IGNS further incorporates a warmup phase to initialize global context, geometric encoding to handle irregular meshes, and a multi-step training objective that facilitates PDE matching, where the trajectory produced by integrating the port-Hamiltonian core aligns with the ground-truth trajectory, thereby reducing rollout error. To evaluate these properties systematically, we introduce new benchmarks that target long-range dependencies and challenging external forcing scenarios. Across all tasks, IGNS consistently outperforms state-of-the-art GNSs, achieving higher accuracy and stability under challenging and complex dynamical systems. Our project page: https://thobotics.github.io/neural_pde_matching.

Contact-rich dexterous manipulation with multi-finger hands remains an open challenge in robotics because task success depends on multi-point contacts that continuously evolve and are highly sensitive to object geometry, frictional transitions, and slip. Recently, tactile-informed manipulation policies have shown promise. However, most use tactile signals as additional observations rather than modeling contact state or how their action outputs interact with low-level controller dynamics. We present Contact-Grounded Policy (CGP), a visuotactile policy that grounds multi-point contacts by predicting coupled trajectories of actual robot state and tactile feedback, and using a learned contact-consistency mapping to convert these predictions into executable target robot states for a compliance controller. CGP consists of two components: (i) a conditional diffusion model that forecasts future robot state and tactile feedback in a compressed latent space, and (ii) a learned contact-consistency mapping that converts the predicted robot state-tactile pair into executable targets for a compliance controller, enabling it to realize the intended contacts. We evaluate CGP using a physical four-finger Allegro V5 hand with Digit360 fingertip tactile sensors, and a simulated five-finger Tesollo DG-5F hand with dense whole-hand tactile arrays. Across a range of dexterous tasks including in-hand manipulation, delicate grasping, and tool use, CGP outperforms visuomotor and visuotactile diffusion-policy baselines.

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

Learning humanoid-object interaction requires coordinating whole-body balance, locomotion, and dexterous hand contact to control both robot and object motion. Human demonstrations provide examples of coordinated interaction, but transferring these behaviors to humanoid robots requires learning how to establish and maintain effective contacts under different embodiments and dynamics. We present Weave, a unified framework for learning whole-body dexterous humanoid-object interaction from captured human demonstrations. Weave first converts captured human-object interactions into executable robot-object references through contact-aware retargeting and approach-motion completion. At its core is a contact- and geometry-aware policy that jointly commands 29 body joints and 12 actuated finger joints across multiple objects and interaction sequences. Evaluation across nine objects yields a 92.5% success rate on trained interactions and, without any additional training, 65.0% on sequences never seen during training. We additionally release ~9,000 physically executed rollouts spanning ~23 hours, providing robot-object trajectories with contact annotations for downstream interaction-policy learning and physically consistent HOI motion generation. Project website: https://xiaohu-art.github.io/Weave/

Recovering ego-camera orientation from manipulation video is a prerequisite for disentangling hand motion from camera motion, a key step in imitation learning from egocentric demonstrations. The obvious approach, inferring orientation from scene geometry, fails when hands occlude the frame: VGGT, a 1B-parameter scene reconstruction model, scores worse than a constant predictor on the TACO benchmark. We identify an alternative visual concept that is present precisely when scene geometry is absent: kinematic coupling dynamics, the structured physical relationship between wrist motion and camera orientation imposed by the arm-shoulder-head chain. We find that this concept is compact (4D inter-wrist features outperform 126D full hand keypoints), temporal (requiring a GRU over short windows rather than per-frame retrieval), and physically grounded (transferring zero-shot across datasets because it is rooted in anatomy rather than scene appearance). Trained only on tabletop manipulation, WristCompass transfers zero-shot to Epic Kitchens cooking video, achieving 14.3^circ median geodesic error and approaching the performance of a 1B-parameter scene model at 200K GRU parameters.

Humans can accomplish complex contact-rich tasks using vision and touch, with highly reactive capabilities such as quick adjustments to environmental changes and adaptive control of contact forces; however, this remains challenging for robots. Existing visual imitation learning (IL) approaches rely on action chunking to model complex behaviors, which lacks the ability to respond instantly to real-time tactile feedback during the chunk execution. Furthermore, most teleoperation systems struggle to provide fine-grained tactile / force feedback, which limits the range of tasks that can be performed. To address these challenges, we introduce TactAR, a low-cost teleoperation system that provides real-time tactile feedback through Augmented Reality (AR), along with Reactive Diffusion Policy (RDP), a novel slow-fast visual-tactile imitation learning algorithm for learning contact-rich manipulation skills. RDP employs a two-level hierarchy: (1) a slow latent diffusion policy for predicting high-level action chunks in latent space at low frequency, (2) a fast asymmetric tokenizer for closed-loop tactile feedback control at high frequency. This design enables both complex trajectory modeling and quick reactive behavior within a unified framework. Through extensive evaluation across three challenging contact-rich tasks, RDP significantly improves performance compared to state-of-the-art visual IL baselines through rapid response to tactile / force feedback. Furthermore, experiments show that RDP is applicable across different tactile / force sensors. Code and videos are available on https://reactive-diffusion-policy.github.io.

We present a boundary integral equation (BIE) framework for two-dimensional time-harmonic elastic transmission problems. Using the Helmholtz decomposition, the elastodynamic displacement fields are expressed in terms of scalar pressure and shear potentials, so that only the four classical Helmholtz boundary integral operators are needed. The key step is a rewriting of the Navier traction operator in the local normal--tangential frame of the interface, in which second-order normal derivatives are eliminated in favour of tangential derivatives and curvature terms. This leads to a one-parameter family of indirect combined field integral equations, depending on a coupling constant αne 0, which we prove to be uniquely solvable. The principal part of the resulting operator is, however, defective, and the discretized systems are severely ill-conditioned. Using the pseudodifferential calculus of the Helmholtz BIOs, we construct explicit left and right analytical preconditioners and prove that the preconditioned operator is a compact perturbation of the identity. Numerical experiments based on high-order Nyström discretizations confirm that the preconditioner clusters the spectrum: the number of GMRES iterations becomes independent of the discretization and is reduced by one order of magnitude or more, also in the high-frequency regime and for non-convex scatterers.

Incremental Potential Contact (IPC) guarantees intersection-free simulation but suffers from high computational costs due to the expensive Hessian assembly and linear solves required by Newton's method. While Preconditioned Nonlinear Conjugate Gradient (PNCG) avoids Hessian assembly, it has historically struggled with poor convergence in stiff, contact-rich scenarios due to the lack of effective preconditioners; simple Jacobi preconditioners fail to capture the global coupling, while advanced hierarchy-based preconditioners like Multilevel Additive Schwarz (MAS) are computationally prohibitive to rebuild at every nonlinear iteration. We present MAS-PNCG, a method that unlocks the power of hierarchical preconditioning for nonlinear optimization. Our key technical innovation is a Sparse-Input Woodbury update algorithm that incrementally adapts the fine-level MAS components to rapidly evolving contact sets. This bypasses the need for full preconditioner rebuilds, reducing maintenance cost to near-zero while capturing the complex spectral properties of the contact system. Furthermore, we replace heuristic PNCG search directions with a Hessian-aware 2D subspace minimization that optimally combines the preconditioned gradient and previous direction. We also apply a fast per-subdomain conservative CCD method that ensures penetration-free trajectories while avoiding overly restrictive global step sizes. Experiments demonstrate that our MAS-PNCG outperforms state-of-the-art Newton-PCG solvers, GIPC and StiffGIPC, both preconditioned with MAS up to 5.66times and 2.07times respectively.

Realistic simulation of dynamic scenes requires accurately capturing diverse material properties and modeling complex object interactions grounded in physical principles. However, existing methods are constrained to basic material types with limited predictable parameters, making them insufficient to represent the complexity of real-world materials. We introduce a novel approach that leverages multi-modal foundation models and video diffusion to achieve enhanced 4D dynamic scene simulation. Our method utilizes multi-modal models to identify material types and initialize material parameters through image queries, while simultaneously inferring 3D Gaussian splats for detailed scene representation. We further refine these material parameters using video diffusion with a differentiable Material Point Method (MPM) and optical flow guidance rather than render loss or Score Distillation Sampling (SDS) loss. This integrated framework enables accurate prediction and realistic simulation of dynamic interactions in real-world scenarios, advancing both accuracy and flexibility in physics-based simulations.

The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number examples with spatially varying diffusion coefficients. We also derive path integral representations for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method's ability to learn constitutive laws from videos.

The elastic response of mechanical, chemical, and biological systems is often modeled using a discrete arrangement of Hookean springs, either representing finite material elements or even the molecular bonds of a system. However, to date, there is no direct derivation of the relation between a general discrete spring network, with arbitrary geometry, and it's corresponding elastic continuum. Furthermore, understanding the network's mechanical response requires simulations that may be expensive computationally. Here we report a method to derive the exact elastic continuum model of any discrete network of springs, requiring network geometry and topology only. We identify and calculate the so-called "non-affine" displacements. Explicit comparison of our calculations to simulations of different crystalline and disordered configurations, shows we successfully capture the mechanics even of auxetic materials. Our method is valid for residually stressed systems with non-trivial geometries, and is an essential step in generalizing active stresses on such discrete systems. It is easily generalizable to other discrete models, and opens the possibility of a rational design of elastic systems.

We investigate the coupling effects of the two-phase interface, viscosity ratio, and density ratio of the dispersed phase to the continuous phase on the flow statistics in two-phase Taylor-Couette turbulence at a system Reynolds number of 6000 and a system Weber number of 10 using interface-resolved three-dimensional direct numerical simulations with the volume-of-fluid method. Our study focuses on four different scenarios: neutral droplets, low-viscosity droplets, light droplets, and low-viscosity light droplets. We find that neutral droplets and low-viscosity droplets primarily contribute to drag enhancement through the two-phase interface, while light droplets reduce the system's drag by explicitly reducing Reynolds stress due to the density dependence of Reynolds stress. Additionally, low-viscosity light droplets contribute to greater drag reduction by further reducing momentum transport near the inner cylinder and implicitly reducing Reynolds stress. While interfacial tension enhances turbulent kinetic energy (TKE) transport, drag enhancement is not strongly correlated with TKE transport for both neutral droplets and low-viscosity droplets. Light droplets primarily reduce the production term by diminishing Reynolds stress, whereas the density contrast between the phases boosts TKE transport near the inner wall. Therefore, the reduction in the dissipation rate is predominantly attributed to decreased turbulence production, causing drag reduction. For low-viscosity light droplets, the production term diminishes further, primarily due to their greater reduction in Reynolds stress, while reduced viscosity weakens the density difference's contribution to TKE transport near the inner cylinder, resulting in a more pronounced reduction in the dissipation rate and consequently stronger drag reduction. Our findings provide new insights into the turbulence modulation in two-phase flow.

Effective control and prediction of dynamical systems often require appropriate handling of continuous-time and discrete, event-triggered processes. Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism for dynamical systems subject to discrete, possibly stochastic, state jumps and multi-modal continuous-time flows. Despite the versatility and importance of SHSs across applications, a general procedure for the explicit learning of both discrete events and multi-mode continuous dynamics remains an open problem. This work introduces Neural Hybrid Automata (NHAs), a recipe for learning SHS dynamics without a priori knowledge on the number of modes and inter-modal transition dynamics. NHAs provide a systematic inference method based on normalizing flows, neural differential equations and self-supervision. We showcase NHAs on several tasks, including mode recovery and flow learning in systems with stochastic transitions, and end-to-end learning of hierarchical robot controllers.

Text-to-image and personalized editing models now synthesize high-fidelity single-subject images with ease. Yet placing multiple named people into shared contact actions such as embrace, carry, or grapple still exposes major failures: fused limbs, invented extremities, and interpenetrating bodies. Existing evaluations largely overlook these anatomical and geometric issues, and VLM-as-a-judge checklists often saturate on Interaction while the errors remain obvious to humans. We introduce MPIE-Bench, a 2,500-sample benchmark of video-mined editing triplets spanning 405 scenes, 14 interaction categories, and four contact densities (C0-C3). We also propose MPIE-Eval, whose two new axes score contact-time geometry from a frozen public multi-person mesh reconstruction. Anatomy asks whether every human-like mass is explained by a complete set of reconstructed bodies, and Interaction asks whether the penetration and surface distance between those bodies match the contact the instruction asked for. Across ten editors, mesh Anatomy tops out at 0.65 and mesh Interaction at 0.72 on two different models, so no single editor is strong on both, while VLM checklists rate the same images above 0.95. A five-rater study confirms that both axes track human judgement more closely than a zero-shot VLM judge, and the rankings hold under ablation of every weight and threshold.

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks. While these methods offer theoretical guarantees, they face two key limitations: (i) they primarily model local relations between adjacent time steps, overlooking longer-range or higher-level physical interactions, and (ii) they focus on forward simulation while neglecting broader physical reasoning tasks. We propose the Denoising Hamiltonian Network (DHN), a novel framework that generalizes Hamiltonian mechanics operators into more flexible neural operators. DHN captures non-local temporal relationships and mitigates numerical integration errors through a denoising mechanism. DHN also supports multi-system modeling with a global conditioning mechanism. We demonstrate its effectiveness and flexibility across three diverse physical reasoning tasks with distinct inputs and outputs.

In this study, we propose a multi branched network approach to predict the dynamics of a physics attractor characterized by intricate and chaotic behavior. We introduce a unique neural network architecture comprised of Radial Basis Function (RBF) layers combined with an attention mechanism designed to effectively capture nonlinear inter-dependencies inherent in the attractor's temporal evolution. Our results demonstrate successful prediction of the attractor's trajectory across 100 predictions made using a real-world dataset of 36,700 time-series observations encompassing approximately 28 minutes of activity. To further illustrate the performance of our proposed technique, we provide comprehensive visualizations depicting the attractor's original and predicted behaviors alongside quantitative measures comparing observed versus estimated outcomes. Overall, this work showcases the potential of advanced machine learning algorithms in elucidating hidden structures in complex physical systems while offering practical applications in various domains requiring accurate short-term forecasting capabilities.

Recent advances integrate physically grounded Newtonian dynamics with neural rendering frameworks, narrowing the gap between photorealistic scene reconstruction and physics-based animation. However, existing approaches focus on mechanically driven dynamics while neglecting temperature, a fundamental yet invisible physical factor underlying phenomena such as melting, solidification, and other thermomechanical processes. In this paper, we propose MeGAS, a novel framework that incorporates thermomechanical phase-change dynamics into 3D Gaussian Splatting (3DGS). Specifically, we propose a new thermomechanical dynamic Gaussian Splatting representation that augments 3DGS with temperature attributes and employs a heat advection-diffusion solver with MPM dynamics incorporating phase transitions, enabling physically plausible and visually realistic synthesis of thermophysical phenomena. Furthermore, a new topology-adaptive Gaussian rendering strategy is proposed to mitigate cracking and floaters under extreme deformation. Extensive experiments demonstrate that MeGAS produces physically consistent thermomechanical behavior while maintaining high-fidelity photorealistic rendering, advancing toward physics-integrated world models.

Soot is a component of atmospheric aerosols that affects climate by scattering and absorbing the sunlight. Soot particles are fractal aggregates composed of elemental carbon. In the atmosphere, the aggregates acquire coatings by condensation and coagulation, resulting in significant compaction of the aggregates that changes the direct climate forcing of soot. Currently, no models exist to rigorously describe the process of soot restructuring, reducing prediction accuracy of atmospheric aerosol models. We develop a discrete element method contact model to simulate restructuring of fractal soot aggregates, represented as assemblies of spheres joined by cohesion and by sintered necks. The model is parametrized based on atomic force spectroscopy data and is used to simulate soot restructuring, showing that the fraction of necks in aggregates determines the restructuring pathway. Aggregates with fewer necks undergo local compaction, while aggregates with nearly-full necking prefer global compaction. Additionally, full compaction occurs within tens of nanoseconds, orders of magnitude faster than the time scale of soot aging through condensation. An important implication is that in atmospheric soot aggregates, the rate of condensation determines how many necks are fractured simultaneously, affecting the restructuring pathway, e.g., producing highly compact, thinly-coated soot as observed in recent studies.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

Robotic grasping and surface exploration benefit from simultaneous measurement of normal and tangential forces and from surface information obtained through contact. Here, we present a compact magnetociliary tactile sensor (MagCilia) that combines a flexible magnetic-cilia structure with a Hall sensor for 3D force sensing. Quasi-static finite element analysis is used to investigate structural deformation and magnetic responses under multidirectional loading. To reconstruct forces from the coupled magnetic channels, we propose causal history fusion regression (CHFR), which combines current magnetic-field measurements with their recent changes. Five-fold cross-validation grouped by calibration record yields root-mean-square errors of 0.40, 0.57, and 0.69 N for Fx, Fy, and Fz, respectively, with corresponding coefficients of determination of 0.93, 0.90, and 0.92. Robotic experiments demonstrate tangential-force-guided gripper adjustment and multi-axis load monitoring under external perturbations. Frequency-domain features of the reconstructed forces distinguish six surface categories with 99.39% accuracy in three-fold cross-validation grouped by acquisition session. An online robotic demonstration additionally identifies all six tested surfaces. These results demonstrate 3D force reconstruction, grasping feedback, and surface recognition using a single compact tactile unit.

The dynamics of materials failure is one of the most critical phenomena in a range of scientific and engineering fields, from healthcare to structural materials to transportation. In this paper we propose a specially designed deep neural network, DyFraNet, which can predict dynamic fracture behaviors by identifying a complete history of fracture propagation - from cracking onset, as a crack grows through the material, modeled as a series of frames evolving over time and dependent on each other. Furthermore, this model can not only forecast future fracture processes but also backcast to elucidate the past fracture history. In this scenario, once provided with the outcome of a fracture event, the model will elucidate past events that led to this state and will predict the future evolution of the failure process. By comparing the predicted results with atomistic-level simulations and theory, we show that DyFraNet can capture dynamic fracture mechanics by accurately predicting how cracks develop over time, including measures such as the crack speed, as well as when cracks become unstable. We use GradCAM to interpret how DyFraNet perceives the relationship between geometric conditions and fracture dynamics and we find DyFraNet pays special attention to the areas around crack tips, which have a critical influence in the early stage of fracture propagation. In later stages, the model pays increased attention to the existing or newly formed damage distribution in the material. The proposed approach offers significant potential to accelerate the exploration of the dynamics in material design against fracture failures and can be beneficially adapted for all kinds of dynamical engineering problems.

Developing world models that understand complex physical interactions is essential for advancing robotic planning and simulation.However, existing methods often struggle to accurately model the environment under conditions of data scarcity and complex contact-rich dynamic motion.To address these challenges, we propose ContactGaussian-WM, a differentiable physics-grounded rigid-body world model capable of learning intricate physical laws directly from sparse and contact-rich video sequences.Our framework consists of two core components: (1) a unified Gaussian representation for both visual appearance and collision geometry, and (2) an end-to-end differentiable learning framework that differentiates through a closed-form physics engine to infer physical properties from sparse visual observations.Extensive simulations and real-world evaluations demonstrate that ContactGaussian-WM outperforms state-of-the-art methods in learning complex scenarios, exhibiting robust generalization capabilities.Furthermore, we showcase the practical utility of our framework in downstream applications, including data synthesis and real-time MPC.

Most learned dexterous grasp generators relegate contact forces to a downstream verification step, so a kinematically-plausible pose can still violate the conditions for a stable physical grasp. We address this with EquiDexFlow, an SE(3)-equivariant flow-matching model that jointly predicts wrist pose, joint angles, fingertip contacts, surface normals, and contact forces from an object point cloud. Our architecture projects contacts onto the object surface and forces into the Coulomb friction cone by construction, so placement and friction compliance hold without loss penalties. We prove end-to-end SE(3) equivariance and verify it empirically over 200 rotations, with wrist residuals below 0.04^circ and exactly zero joint deviation. Trained on 8,100 force-closure grasps across 81 objects for the 16-DoF Allegro Hand, our model achieves zero friction violations, the best composite score, and the lowest wrench residual among all ablation variants. We retarget decoded fingertip contacts to a 16-DoF LEAP Hand via per-finger inverse kinematics, and our hardware-feasible refinement places every joint at least 5% inside its actuator envelope while preserving wrench balance. On the physical robot, retargeted EquiDexFlow-decoded grasps complete open-loop pick-and-hold trials on all six test objects, with every asymmetric object succeeding at both the canonical pose and a 120^circ co-rotation. Videos, code, and checkpoints are available at https://equidexflow.github.io.

Achieving robust coordination and cooperation is a central challenge in multi-agent reinforcement learning (MARL). Uncovering the mechanisms underlying such emergent behaviors calls for a dynamical understanding of learn processes. In this work, we investigate the dynamics of actor-critic agents in stochastic games, focusing on the impact of entropy regularization. By leveraging time-scale separation, we derive the system's evolution equations, which are then formally analyzed using dynamical systems theory. We find that in the constant-sum game of Matching Pennies, the system exhibits chaotic behavior. Entropy regularization mitigates this chaos and drives the dynamics toward convergence to fair cooperation. In contrast, in the general-sum game of the Prisoner's Dilemma, the system displays multistability. Interestingly, the three stable equilibria of the system correspond to the well-known ALLC (Always Cooperate), ALLD (Always Defect), and GRIM (Grim Trigger) strategies from evolutionary game theory (EGT). Entropy regularization strengthens system resilience by enlarging the basin of attraction of the cooperative equilibrium. Our findings reveal a close link between the mechanism of direct reciprocity in EGT and how cooperation emerges in MARL, offering insights for designing more robust and collaborative multi-agent systems.

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.

We report a flexible multi-modal mechanics language model, MeLM, applied to solve various nonlinear forward and inverse problems, that can deal with a set of instructions, numbers and microstructure data. The framework is applied to various examples including bio-inspired hierarchical honeycomb design, carbon nanotube mechanics, and protein unfolding. In spite of the flexible nature of the model-which allows us to easily incorporate diverse materials, scales, and mechanical features-it performs well across disparate forward and inverse tasks. Based on an autoregressive attention-model, MeLM effectively represents a large multi-particle system consisting of hundreds of millions of neurons, where the interaction potentials are discovered through graph-forming self-attention mechanisms that are then used to identify relationships from emergent structures, while taking advantage of synergies discovered in the training data. We show that the model can solve complex degenerate mechanics design problems and determine novel material architectures across a range of hierarchical levels, providing an avenue for materials discovery and analysis. Looking beyond the demonstrations reported in this paper, we discuss other opportunities in applied mechanics and general considerations about the use of large language models in modeling, design, and analysis that can span a broad spectrum of material properties from mechanical, thermal, optical, to electronic.

The transition of an impulsively excited kink oscillation of a solar coronal loop to an oscillation with a stationary amplitude, i.e., the damping pattern, is determined using the low-dimensional self-oscillation model. In the model, the decayless kink oscillations are sustained by the interaction of the oscillating loop with an external quasi-steady flow. The analytical solution is based on the assumption that the combined effect of the effective dissipation, for example, by resonant absorption, and interaction with an external flow, is weak. The effect is characterised by a dimensionless coupling parameter. The damping pattern is found to depend upon the initial amplitude and the coupling parameter. The approximate expression shows a good agreement with a numerical solution of the self-oscillation equation. The plausibility of the established damping pattern is demonstrated by an observational example. Notably, the damping pattern is not exponential, and the characteristic decay time is different from the time determined by the traditionally used exponential damping fit. Implications of this finding for seismology of the solar coronal plasmas are discussed. In particular, it is suggested that a very rapid, in less than the oscillation period, decay of the oscillation to the stationary level, achieved for larger values of the coupling parameter, can explain the relative rareness of the kink oscillation events.