Daily Papers

Vision-language models (VLMs) are increasingly used as automated judges for multimodal and embodied tasks, yet aggregate accuracy or consistency alone does not reveal whether a judge changes its verdict for the right reason. We propose State-Conditional Invariance (SCI), a reliability principle requiring a judge to remain stable under semantics-preserving changes in presentation while responding to causal interventions that change the task outcome. We instantiate SCI in GridWM-Judge, a simulator-grounded diagnostic benchmark built from deterministic MiniGrid trajectories with aligned Full, evidence-removal, and counterfactual variants, plus presentation and representation probes. Across five diagnostic tasks, GridWM-Judge tests local perception, action-conditioned transitions, presentation stability, representation exchangeability, and Full-CF causal discrimination. Our diagnostic evaluations reveal heterogeneous failure modes, including sensitivity to evidence presentation and encoding, low activation on successful trajectories, and weak paired counterfactual discrimination. Perception-controlled analyses further indicate that visual grounding and objective recovery are substantial, model-dependent bottlenecks. These results motivate jointly reporting correctness, presentation stability, and causal sensitivity instead of relying on a single score.

We present XLand-MiniGrid, a suite of tools and grid-world environments for meta-reinforcement learning research inspired by the diversity and depth of XLand and the simplicity and minimalism of MiniGrid. XLand-Minigrid is written in JAX, designed to be highly scalable, and can potentially run on GPU or TPU accelerators, democratizing large-scale experimentation with limited resources. To demonstrate the generality of our library, we have implemented some well-known single-task environments as well as new meta-learning environments capable of generating 10^8 distinct tasks. We have empirically shown that the proposed environments can scale up to 2^{13} parallel instances on the GPU, reaching tens of millions of steps per second.

One of the key challenges of Reinforcement Learning (RL) is the ability of agents to generalise their learned policy to unseen settings. Moreover, training RL agents requires large numbers of interactions with the environment. Motivated by the recent success of Offline RL and Imitation Learning (IL), we conduct a study to investigate whether agents can leverage offline data in the form of trajectories to improve the sample-efficiency in procedurally generated environments. We consider two settings of using IL from offline data for RL: (1) pre-training a policy before online RL training and (2) concurrently training a policy with online RL and IL from offline data. We analyse the impact of the quality (optimality of trajectories) and diversity (number of trajectories and covered level) of available offline trajectories on the effectiveness of both approaches. Across four well-known sparse reward tasks in the MiniGrid environment, we find that using IL for pre-training and concurrently during online RL training both consistently improve the sample-efficiency while converging to optimal policies. Furthermore, we show that pre-training a policy from as few as two trajectories can make the difference between learning an optimal policy at the end of online training and not learning at all. Our findings motivate the widespread adoption of IL for pre-training and concurrent IL in procedurally generated environments whenever offline trajectories are available or can be generated.

Artificial Intelligence (AI) data centers are emerging as converter-dominated, parameter-rich electrical systems whose dynamic response depends on fast workload-driven demand variations, tightly regulated data-hall converters, and coordinated on-site sources. Assessing such systems by repeatedly solving nonlinear time-domain models for every outage, load realization, and parameter perturbation is computationally expensive and provides limited insight into response sensitivity. This paper presents a trajectory sensitivity (TS)-based dynamic assessment framework for a self-contained AI data center supplied by a 2 kV DC microgrid with a grid-tied interface. The model includes time-varying data-hall load profiles, a voltage source converter (VSC), battery energy storage systems (BESS) units, supercapacitors, and synchronous-generation-side sources. For each disturbance, firstly, TS are computed along the nonlinear disturbance trajectory, capturing the local effect of source trips, data-hall outages, converter controls, and load ramps. Later, the computed TS data is used to estimate system trajectories under simultaneous parameter perturbations. Validation against full nonlinear ODE simulations with pm 15% perturbations shows close agreement. In addition, the TS-based approach reduces computational time of dynamic-response evaluations from seconds to milliseconds, demonstrating its potential as a scalable screening tool for AI data center dynamics.

We consider the problem of forecasting motion from a single image, i.e., predicting how objects in the world are likely to move, without the ability to observe other parameters such as the object velocities or the forces applied to them. We formulate this task as conditional generation of dense trajectory grids with a model that closely follows the architecture of modern video generators but outputs motion trajectories instead of pixels. This approach captures scene-wide dynamics and uncertainty, yielding more accurate and diverse predictions than prior regressors and generators. We extensively evaluate our method on simulated data, demonstrate its effectiveness on downstream applications such as robotics, and show promising accuracy on real-world intuitive physics datasets. Although recent state-of-the-art video generators are often regarded as world models, we show that they struggle with forecasting motion from a single image, even in simple physical scenarios such as falling blocks or mechanical object interactions, despite fine-tuning on such data. We show that this limitation arises from the overhead of generating pixels rather than directly modeling motion.

Training competitive deep video models is an order of magnitude slower than training their counterpart image models. Slow training causes long research cycles, which hinders progress in video understanding research. Following standard practice for training image models, video model training assumes a fixed mini-batch shape: a specific number of clips, frames, and spatial size. However, what is the optimal shape? High resolution models perform well, but train slowly. Low resolution models train faster, but they are inaccurate. Inspired by multigrid methods in numerical optimization, we propose to use variable mini-batch shapes with different spatial-temporal resolutions that are varied according to a schedule. The different shapes arise from resampling the training data on multiple sampling grids. Training is accelerated by scaling up the mini-batch size and learning rate when shrinking the other dimensions. We empirically demonstrate a general and robust grid schedule that yields a significant out-of-the-box training speedup without a loss in accuracy for different models (I3D, non-local, SlowFast), datasets (Kinetics, Something-Something, Charades), and training settings (with and without pre-training, 128 GPUs or 1 GPU). As an illustrative example, the proposed multigrid method trains a ResNet-50 SlowFast network 4.5x faster (wall-clock time, same hardware) while also improving accuracy (+0.8% absolute) on Kinetics-400 compared to the baseline training method. Code is available online.

We present a novel data-driven simulation environment for modeling traffic in metropolitan street intersections. Using real-world tracking data collected over an extended period of time, we train trajectory forecasting models to learn agent interactions and environmental constraints that are difficult to capture conventionally. Trajectories of new agents are first coarsely generated by sampling from the spatial and temporal generative distributions, then refined using state-of-the-art trajectory forecasting models. The simulation can run either autonomously, or under explicit human control conditioned on the generative distributions. We present the experiments for a variety of model configurations. Under an iterative prediction scheme, the way-point-supervised TrajNet++ model obtained 0.36 Final Displacement Error (FDE) in 20 FPS on an NVIDIA A100 GPU.

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners.

Micro Aerial Vehicles (MAVs) that operate in unstructured, unexplored environments require fast and flexible local planning, which can replan when new parts of the map are explored. Trajectory optimization methods fulfill these needs, but require obstacle distance information, which can be given by Euclidean Signed Distance Fields (ESDFs). We propose a method to incrementally build ESDFs from Truncated Signed Distance Fields (TSDFs), a common implicit surface representation used in computer graphics and vision. TSDFs are fast to build and smooth out sensor noise over many observations, and are designed to produce surface meshes. Meshes allow human operators to get a better assessment of the robot's environment, and set high-level mission goals. We show that we can build TSDFs faster than Octomaps, and that it is more accurate to build ESDFs out of TSDFs than occupancy maps. Our complete system, called voxblox, will be available as open source and runs in real-time on a single CPU core. We validate our approach on-board an MAV, by using our system with a trajectory optimization local planner, entirely on-board and in real-time.

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of them (such as finding their intersections) can be done offline. At runtime we quickly generate a smooth path between given initial and terminal positions. Our algorithm designs trajectories that are guaranteed to be safe at all times, and detects infeasibility whenever such a trajectory does not exist. Our algorithm is based on two subproblems that we can solve very efficiently: finding a shortest path in a weighted graph, and solving (multiple) convex optimal-control problems. We demonstrate the proposed path planner on large-scale numerical examples, and we provide an efficient open-source software implementation, fastpathplanning.

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

Generative models have gained significant traction in offline reinforcement learning (RL) due to their ability to model complex trajectory distributions. However, existing generation-based approaches still struggle with long-horizon tasks characterized by sparse rewards. Some hierarchical generation methods have been developed to mitigate this issue by decomposing the original problem into shorter-horizon subproblems using one policy and generating detailed actions with another. While effective, these methods often overlook the multi-scale temporal structure inherent in trajectories, resulting in suboptimal performance. To overcome these limitations, we propose MAGE, a Multi-scale Autoregressive GEneration-based offline RL method. MAGE incorporates a condition-guided multi-scale autoencoder to learn hierarchical trajectory representations, along with a multi-scale transformer that autoregressively generates trajectory representations from coarse to fine temporal scales. MAGE effectively captures temporal dependencies of trajectories at multiple resolutions. Additionally, a condition-guided decoder is employed to exert precise control over short-term behaviors. Extensive experiments on five offline RL benchmarks against fifteen baseline algorithms show that MAGE successfully integrates multi-scale trajectory modeling with conditional guidance, generating coherent and controllable trajectories in long-horizon sparse-reward settings.

Future planetary exploration rovers must operate for extended durations on hybrid power inputs that combine steady radioisotope thermoelectric generator (RTG) output with variable solar photovoltaic (PV) availability. While energy-aware planning has been studied for aerial and underwater robots under battery limits, few works for ground rovers explicitly model power flow or enforce instantaneous power constraints. Classical terrain-aware planners emphasize slope or traversability, and trajectory optimization methods typically focus on geometric smoothness and dynamic feasibility, neglecting energy feasibility. We present an energy-constrained trajectory planning framework that explicitly integrates physics-based models of translational, rotational, and resistive power with baseline subsystem loads, under hybrid RTG-solar input. By incorporating both cumulative energy budgets and instantaneous power constraints into SE(2)-based polynomial trajectory optimization, the method ensures trajectories that are simultaneously smooth, dynamically feasible, and power-compliant. Simulation results on lunar-like terrain show that our planner generates trajectories with peak power within 0.55 percent of the prescribed limit, while existing methods exceed limits by over 17 percent. This demonstrates a principled and practical approach to energy-aware autonomy for long-duration planetary missions.

We present Mini-BEHAVIOR, a novel benchmark for embodied AI that challenges agents to use reasoning and decision-making skills to solve complex activities that resemble everyday human challenges. The Mini-BEHAVIOR environment is a fast, realistic Gridworld environment that offers the benefits of rapid prototyping and ease of use while preserving a symbolic level of physical realism and complexity found in complex embodied AI benchmarks. We introduce key features such as procedural generation, to enable the creation of countless task variations and support open-ended learning. Mini-BEHAVIOR provides implementations of various household tasks from the original BEHAVIOR benchmark, along with starter code for data collection and reinforcement learning agent training. In essence, Mini-BEHAVIOR offers a fast, open-ended benchmark for evaluating decision-making and planning solutions in embodied AI. It serves as a user-friendly entry point for research and facilitates the evaluation and development of solutions, simplifying their assessment and development while advancing the field of embodied AI. Code is publicly available at https://github.com/StanfordVL/mini_behavior.

Generating high-fidelity synthetic GPS trajectories is increasingly important for applications in transportation, urban planning, and what-if scenario simulation, especially as privacy concerns limit access to real-world mobility data. Existing trajectory generation models face a trade-off between efficiency and faithfulness to road network topology: continuous-space methods enable fast generation but ignore the road network, while topology-aware approaches rely on search-based autoregressive decoding that limits generation speed. We propose TrajDLM, a topology-aware trajectory generation framework based on block diffusion language models that bridges this gap. TrajDLM models trajectories as sequences of discrete road segments, combining a block diffusion backbone for efficient denoising, topology-aware embeddings from a road network encoder, and topology-constrained sampling to ensure coherent and realistic trajectories. Across three city-scale datasets, TrajDLM achieves strong performance on fine-grained local similarity metrics while being up to 2.8times faster than prior work, and demonstrates strong zero-shot transfer across domains, including unseen transportation modes. These results highlight the effectiveness of block-wise discrete diffusion as a scalable approach to accurate and efficient trajectory generation. Our code is available at https://github.com/cruiseresearchgroup/TrajDLM/

Mobility simulation supports logistics, safety, and communications planning in industrial environments such as ports, mines, and airports. Existing trajectory models, however, rely on absolute coordinates, road-network tokens, or semantic zones: representations that are site-specific and not well suited to unstructured industrial terrain. We introduce the Industrial Kinematic Trajectory Model (IKTM), a coordinate-free trajectory generator that represents industrial vehicle motion through kinematic sequences (speed and heading change) with no absolute spatial reference. IKTM uses an autoregressive causal transformer with probabilistic mixture heads and extends our prior coordinate-free Markovian model with deep sequence modelling and an explicit duration-conditioning signal. Trained on one site and evaluated zero-shot on three unseen sites, it matches the small-turn shape of the empirical turn-rate distributions of held-out telematics; across all four sites, the per-site mean Jensen-Shannon divergence over 100 sampling seeds spans approximately 0.035-0.050 bits under an oracle-length duration-target protocol and approximately 0.032-0.042 bits under a fully zero-shot prior-length protocol, with similar ranges whether out-of-distribution (OOD) duration targets are drawn from each held-out site's empirical length distribution or from the Site A prior. Both protocols stay above the metric's sampling-noise floor (<=0.0049 bits). Paired by site, the oracle-length values are 5.3-6.0x lower than those of a re-implementation of our prior Markovian model under the same 1 Hz protocol. Termination is duration-conditioned rather than spatial: rollouts stop on 100% of trials with a length-tracking error of +0.0 +/- 0.0 s against the sampled target (100 of 100 exactly on target; N=100, T=0.2, untouched in-distribution test split).

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Advances in time-resolved Particle Tracking Velocimetry (4D-PTV) techniques have been consistently revealed more accurate Lagrangian particle motions. A novel track initialisation technique as a complementary part of 4D-PTV, based on local temporal and spatial coherency of neighbour trajectories, is proposed. The proposed Lagrangian Coherent Track Initialisation (LCTI) applies physics-based Finite Time Lyapunov Exponent (FTLE) to build four frame coherent tracks. We locally determine the boundaries (i.e., ridges) of Lagrangian Coherent Structures (LCS) among neighbour trajectories by using FTLE to distinguish clusters of coherent motions. To evaluate the proposed technique, we created an open-access synthetic Lagrangian and Eulerian dataset of the wake downstream of a smooth cylinder at a Reynolds number equal to 3900 obtained from 3D Direct Numerical Simulation (DNS). The dataset is available to the public. Performance of the proposed method based on three characteristic parameters, temporal scale, particle concentration (i.e., density), and noise ratio, showed robust behaviour in finding true tracks compared to the recent initialisation algorithms. Sensitivity of LCTI to the number of untracked and wrong tracks are also discussed. We address the capability of using the proposed method as a function of a 4D-PTV scheme in the Lagrangian Particle Tracking challenge for a flow with high particle densities. Finally, the LCTI behaviour was assessed in a real jet impingement experiment. LCTI was found to be a reliable tracking tool in complex flow motions, with a strength revealed for flows with high particle concentrations.

This paper proposes a novel sampling-based motion planner, which integrates in RRT* (Rapidly exploring Random Tree star) a database of pre-computed motion primitives to alleviate its computational load and allow for motion planning in a dynamic or partially known environment. The database is built by considering a set of initial and final state pairs in some grid space, and determining for each pair an optimal trajectory that is compatible with the system dynamics and constraints, while minimizing a cost. Nodes are progressively added to the tree of feasible trajectories in the RRT* algorithm by extracting at random a sample in the gridded state space and selecting the best obstacle-free motion primitive in the database that joins it to an existing node. The tree is rewired if some nodes can be reached from the new sampled state through an obstacle-free motion primitive with lower cost. The computationally more intensive part of motion planning is thus moved to the preliminary offline phase of the database construction {at the price of some performance degradation due to gridding. Grid resolution can be tuned so as to compromise between (sub)optimality and size of the database. The planner is shown to be }asymptotically optimal as the grid resolution goes to zero and the number of sampled states grows to infinity.

Deep reinforcement policy learning directly in physical robots (on-robot learning) remains bottlenecked by slow wall-clock training times. We present SymmGrid, a trajectory level augmentation framework inspired by parallelized symmetries that super-scales group transformations to significantly accelerate on-robot learning in both egocentric and exocentric visual setups. We model a Markov Decision Process (MDP) under a symmetry tree, in which state-action pairs have admissible parallelized invariant transformations that yield a geometric grid structure. The state is modelled with ego- or exocentric images and proprioception information. The latter require special treatment, in the form of homographies, to warp visual scenes in line with their corresponding spatial transformations. These parallelized transformations produce a large set of unique symmetric equivalences that populate the replay buffer with diverse and consistent experiences that speed up learning and improve performance. We present extensive training and evaluations performed directly on real robot manipulation contact tasks including peg-insertions, cable routing, and object relocations. Relative to SOTA, SymmGrid achieved wall-clock training convergence speed-ups of 1.37-2.17x, evaluation success rate improvements of 1.09x-1.27x, fastest training convergence times of 16.6, 10.9, and 79.3 minutes respectively. For trajectory wide assessments, we used normalized area under the curve (nAUC) ratios. SymmGrid achieved improvements of up to 2.59x. These results confirm that simple branch symmetries can have an outsized result due to super-scaling and bring us closer to sub-10 minute on-robot learning training in manipulation tasks suitable for arms and humanoids. The project page is available at symmgrid-robot.github.io

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

Data-driven surrogate modeling has emerged as a powerful paradigm for accelerating computational fluid dynamics, and hierarchical U-shaped networks, which resemble the structure of classical Geometric Multigrid (GMG) methods, have become prevalent designs. Modern surrogates built on these designs achieve competitive accuracy at a fraction of the cost of numerical solvers; however, accurate prediction of complex flows remains challenging, and no existing architecture leads across them. In such networks, the multigrid analogy mainly concerns the multi-resolution topology, while their components largely follow common vision practice. To address this, this study introduces SUMNO, a multigrid neural operator for fluid flow fields on regular grids that spatially unrolls a V-cycle into a feed-forward U-shaped network. Parameter-free down- and upsampling stand in for restriction and prolongation, and additive skip connections for coarse-grid correction, with normalization-free transfer and skip pathways. Within this macro-architecture, convolutions are used at the fine and intermediate resolutions and shifted-window attention at the coarsest, whose window partitioning is generalized to handle periodicity independently per axis. Evaluated on unseen test configurations across four unsteady and steady flow benchmarks against five representative baselines, SUMNO is best in 5 of 7 settings and ranks second in the remaining two. It reduces the 10-step rollout MSE by about 30% relative to the strongest baseline, and outperforms three baselines with over 130 million parameters using 9.4 million parameters.

In urban low-altitude flight, buildings reshape ambient wind into spatially varying 3D flow, making unmanned aerial vehicle (UAV) energy depend on local wind exposure as well as path length. However, building-resolved wind information is rarely available when a mission must be planned. Computational fluid dynamics (CFD) can produce high-fidelity urban flow fields, but each simulation is tied to a fixed inflow boundary condition and can take hours to days, which is incompatible with urban UAV missions that typically last minutes to tens of minutes. We present GeoWind2Plan, a geometry-to-wind-to-planning framework for mission-time 3D urban wind prediction and energy-efficient UAV planning. Given only a background wind vector, 3D building geometry, and a start-goal pair, GeoWind2Plan transforms the building geometry into a reference-wind frame, predicts mission-relevant 3D wind patches with a localized geometry-conditioned neural operator, stitches them into a queryable local wind field, and optimizes a feasible 3D path and speed profile using a physically grounded UAV energy model. Rather than pursuing CFD-perfect reconstruction, GeoWind2Plan targets decision-useful wind prediction: trajectories are planned with predicted wind and evaluated under high-fidelity CFD wind. Across held-out urban domains, wind speeds, and mission wind-angle regimes, GeoWind2Plan performs corridor-localized wind inference in about 3 seconds, compared with roughly 8 hours for CFD. Under CFD evaluation, trajectories planned with GeoWind2Plan reduce energy by 6.9%, 12.7%, and 4.5% in tailwind, headwind, and crosswind missions relative to wind-agnostic planning, recovering 87.9%, 85.7%, and 75.0% of CFD-reference savings. These results show that fast, corridor-localized 3D urban wind prediction can make wind-aware UAV energy planning practical at mission time.

Autonomous agents' interactions with humans are increasingly focused on adapting to their changing preferences in order to improve assistance in real-world tasks. Effective agents must learn to accurately infer human goals, which are often hidden, to collaborate well. However, existing Multi-Agent Reinforcement Learning (MARL) environments lack the necessary attributes required to rigorously evaluate these agents' learning capabilities. To this end, we introduce ColorGrid, a novel MARL environment with customizable non-stationarity, asymmetry, and reward structure. We investigate the performance of Independent Proximal Policy Optimization (IPPO), a state-of-the-art (SOTA) MARL algorithm, in ColorGrid and find through extensive ablations that, particularly with simultaneous non-stationary and asymmetric goals between a ``leader'' agent representing a human and a ``follower'' assistant agent, ColorGrid is unsolved by IPPO. To support benchmarking future MARL algorithms, we release our environment code, model checkpoints, and trajectory visualizations at https://github.com/andreyrisukhin/ColorGrid.

Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous differential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization problem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of Bézier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap rounding of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time.

One-step generative models construct a static generator through iterative training-time transport. Existing transport objectives primarily assess distributional motion, although a neural generator needs to realize the requested sample displacements jointly through shared parameter updates. The training-time construction raises the question: once training becomes the iterative process that constructs the final one-step map, what to optimize: the next distributional move, or the route by which the finite generator learns the final map? To address the question, we introduce Training Dynamics Action (TDAction), which selects transport targets according to local shared-parameter realization cost while retaining a prescribed level of distributional progress. We formulate the cost as a soft-terminal control problem and derive a closed-form Batch Tangent Action-to-Go value that accounts for parameter effort and terminal mismatch. The criterion captures cross-sample interactions omitted by independent pairwise costs; under isotropic mobility, the criterion agrees with quadratic Euclidean assignment for deterministic balanced couplings. Randomized tangent probes provide a low-rank implementation that constructs shared detached targets without adding an inference-time trajectory. Controlled studies examine the relationship between generator geometry, transport selection, and realized local action. On ImageNet 256times256, TDAction attains an FID below 1.1 without distillation.

Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical, numerical, and experimental efforts conducted over the past thirty years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence. We propose a machine learning approach, based on a state-of-the-art diffusion model, to generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, thereby bypassing the need for direct numerical simulations or experiments to obtain reliable Lagrangian data. Our model demonstrates the ability to reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law, and the increased intermittency around the dissipative scale. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pre-training various downstream applications of Lagrangian turbulence.

Weather Jiu-Jitsu is a control paradigm for extreme climatological events, inspired by chaos theory. As a proposition, small, precise, targeted, and cost-inexpensive perturbations can redirect trajectories of a large dynamical system. This strategy has been demonstrated analytically in the Lorenz-63 system, where a naturally chaotic trajectory switching between two attractors can be confined to a single attractor, indefinitely, via arbitrarily small perturbations. This paper examines the feasibility of Microsoft's Aurora -- a 1.3 billion parameter global atmospheric model -- as a test bed for this strategy. This paper explores three questions: (1) Is Aurora a reliable enough simulation environment to serve as a meaningful testbed? (2) Are the perturbations required to redirect its trajectories small enough to be physically plausible? (3) Does Aurora's learned latent space (the parametric estimators on climatological attributes) yield any apparent, structured, and/or perhaps interpretable features that can convey a geo/atmospheric response to initial conditions? We find evidence consistent with all three: Aurora's modeled trajectories respond to perturbations beyond measurement drift, the perturbation magnitudes required are small relative to the model's own forecast uncertainty, and its latent representations exhibit directional structure that responds to Jiu-Jitsu-type interventions, even though that structure does not separate extreme from normal states outright. These results should be read as feasibility diagnostics rather than a demonstration of control: we do not implement or test an actual steering intervention on Aurora, and several of our findings, particularly around the model's latent-space geometry, are exploratory.

Modeling human mobility is vital for extensive applications such as transportation planning and epidemic modeling. With the rise of the Artificial Intelligence Generated Content (AIGC) paradigm, recent works explore synthetic trajectory generation using autoregressive and diffusion models. While these methods show promise for generating single-day trajectories, they remain limited by inefficiencies in long-term generation (e.g., weekly trajectories) and a lack of explicit spatiotemporal multi-scale modeling. This study proposes Multi-Scale Spatio-Temporal AutoRegression (M-STAR), a new framework that generates long-term trajectories through a coarse-to-fine spatiotemporal prediction process. M-STAR combines a Multi-scale Spatiotemporal Tokenizer that encodes hierarchical mobility patterns with a Transformer-based decoder for next-scale autoregressive prediction. Experiments on two real-world datasets show that M-STAR outperforms existing methods in fidelity and significantly improves generation speed. The data and codes are available at https://github.com/YuxiaoLuo0013/M-STAR.

It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model continuous dynamics and non-linear paths that entities can take in these systems. To address this issue, we establish a link between continuous normalizing flows and dynamic optimal transport, that allows us to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present TrajectoryNet, which controls the continuous paths taken between distributions to produce dynamic optimal transport. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.

Accurate prediction of Lagrangian trajectories in turbulent flow remains challenging due to limited temporal information in transport functions. This paper shows that surrounding coherent motions sharing the same dynamics carry enough information to provide highly probable trajectories even from sparse temporal observations. The proposed coherent predictor builds on Lagrangian coherent structures (LCSs), the advective transport barriers that govern the cohesive motion of neighbouring particles. Coherent trajectories are quantified using a local segmentation with the finite-time Lyapunov exponents (FTLE). The coherent predictor incorporates information from the particle's position history and neighbouring coherent velocity and acceleration into a novel cost function to predict its trajectory. The proposed cost function follows a physics-informed approach where the position history acts as a data fidelity term and the coherent velocity and acceleration act as physics-based regularisation constraints. We assess our proposed approach using both three-dimensional (3D) synthetic and experimental data of the wake behind a smooth cylinder and two-dimensional (2D) homogeneous isotropic turbulent (HIT) flow. The coherent predictor is deemed generic due to its consistent behaviour regardless of flow dimensions, Reynolds number, and flow topology. Our results show that the optimal cost function parameters can be modelled from the measurement uncertainties, giving lower prediction error and uncertainty than current methods. We see direct signatures of flow topology on the prediction error map, including the cylinder leading edge boundary layer, the sideward shear layers, and the vortex formation structures. These topologies are marked by high Lagrangian gradients and 3D directional motions.

Reinforcement learning (RL) can provide adaptive and scalable controllers essential for power grid decarbonization. However, RL methods struggle with power grids' complex dynamics, long-horizon goals, and hard physical constraints. For these reasons, we present RL2Grid, a benchmark designed in collaboration with power system operators to accelerate progress in grid control and foster RL maturity. Built on RTE France's power simulation framework, RL2Grid standardizes tasks, state and action spaces, and reward structures for a systematic evaluation and comparison of RL algorithms. Moreover, we integrate operational heuristics and design safety constraints based on human expertise to ensure alignment with physical requirements. By establishing reference performance metrics for classic RL baselines on RL2Grid's tasks, we highlight the need for novel methods capable of handling real systems and discuss future directions for RL-based grid control.

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

We present a novel approach for generating motion primitives for kinodynamic motion planning using diffusion models. The motions generated by our approach are adapted to each problem instance by utilizing problem-specific parameters, allowing for finding solutions faster and of better quality. The diffusion models used in our approach are trained on randomly cut solution trajectories. These trajectories are created by solving randomly generated problem instances with a kinodynamic motion planner. Experimental results show significant improvements up to 30 percent in both computation time and solution quality across varying robot dynamics such as second-order unicycle or car with trailer.

The advancement of large language models (LLMs) prompts the development of multi-modal agents, which are used as a controller to call external tools, providing a feasible way to solve practical tasks. In this paper, we propose a multi-modal agent tuning method that automatically generates multi-modal tool-usage data and tunes a vision-language model (VLM) as the controller for powerful tool-usage reasoning. To preserve the data quality, we prompt the GPT-4o mini model to generate queries, files, and trajectories, followed by query-file and trajectory verifiers. Based on the data synthesis pipeline, we collect the MM-Traj dataset that contains 20K tasks with trajectories of tool usage. Then, we develop the T3-Agent via Trajectory Tuning on VLMs for Tool usage using MM-Traj. Evaluations on the GTA and GAIA benchmarks show that the T3-Agent consistently achieves improvements on two popular VLMs: MiniCPM-V-8.5B and {Qwen2-VL-7B}, which outperforms untrained VLMs by 20%, showing the effectiveness of the proposed data synthesis pipeline, leading to high-quality data for tool-usage capabilities.

We introduce a method for generating realistic pedestrian trajectories and full-body animations that can be controlled to meet user-defined goals. We draw on recent advances in guided diffusion modeling to achieve test-time controllability of trajectories, which is normally only associated with rule-based systems. Our guided diffusion model allows users to constrain trajectories through target waypoints, speed, and specified social groups while accounting for the surrounding environment context. This trajectory diffusion model is integrated with a novel physics-based humanoid controller to form a closed-loop, full-body pedestrian animation system capable of placing large crowds in a simulated environment with varying terrains. We further propose utilizing the value function learned during RL training of the animation controller to guide diffusion to produce trajectories better suited for particular scenarios such as collision avoidance and traversing uneven terrain. Video results are available on the project page at https://nv-tlabs.github.io/trace-pace .

Terminal agents are moving beyond local operations toward completing real-world professional tasks. Short trajectories can demonstrate commands and tool calls, but they do not fully show how agents accumulate evidence through exploration, use it to inform judgments, continually adjust strategies based on feedback, and turn intermediate results into final deliverables. High-quality long-horizon trajectories capture these agentic behavioral patterns and their connections within a single problem-solving process, providing richer experience for sustained autonomous work. However, environment synthesis may complete or simplify the key work underlying these patterns in advance and thus remove the need for exploration, implementation, and verification that the agent was meant to perform. To address this, we introduce TerminalHorizon, a fully automated data synthesis engine for long-horizon terminal agents. Starting from real-world professional work, it uses independent execution to identify key work omitted during construction and uses the resulting evidence to guide environment reconstruction. To extend these patterns across stages, it progressively expands tasks under the same goal, introducing new requirements that build on prior results and call for further exploration and improvement. Using this engine, we construct 1.5K task environments and perform supervised fine-tuning of Qwen3.5-27B on the resulting dataset to obtain TerminalHorizon-27B. We achieve substantial performance gains on all 12 benchmarks spanning coding-agent tasks, agentic tasks in real-world production settings, and general reasoning. Multiple RSI case studies, each with a 12-hour research budget, further demonstrate the model's ability to continue experimenting beyond an initial solution, improve its methods based on feedback, and retain effective improvements in its final deliverables.

This work presents an optimization method for generating kinodynamically feasible and collision-free multi-robot trajectories that exploits an incremental denoising scheme in diffusion models. Our key insight is that high-quality trajectories can be discovered merely by denoising noisy trajectories sampled from a distribution. This approach has no learning component, relying instead on only two ingredients: a dynamical model of the robots to obtain feasible trajectories via rollout, and a fitness function to guide denoising with Monte Carlo gradient approximation. The proposed framework iteratively optimizes a deformation for the previous trajectory with the current denoising process, allows anytime refinement as time permits, supports different dynamics, and benefits from GPU acceleration. Our evaluations for differential-drive and holonomic teams with up to 16 robots in 2D and 3D worlds show its ability to discover high-quality solutions faster than other black-box optimization methods such as MPPI. In a 2D holonomic case with 16 robots, it is almost twice as fast. As evidence for feasibility, we demonstrate zero-shot deployment of the planned trajectories on eight multirotors.

Predicting how a dynamical unit evolves over time - how an individual ages, an epidemic spreads, or a physical system degrades - typically requires dense longitudinal tracking. When only extremely sparse or entirely cross-sectional data is available, inferring individualized, continuous-time trajectories is fundamentally ill-posed. Existing methods force a strict compromise: sequence models (e.g. latent ODEs) require dense longitudinal data, while cross-sectional methods (e.g. optimal transport, flow matching-based) map aggregate populations, losing individual dynamics. In this paper, we demonstrate that this dichotomy can be broken. We introduce CADENCE, a principled probabilistic framework that recovers continuous individual trajectories from isolated snapshots by anchoring latent dynamics to static, individual-level contexts. We provide novel identifiability guarantees for single-timepoint trajectory inference. By combining a score-based spatial encoder (bijective Probability Flow ODE) to eliminate diffeomorphic ambiguities with a Soft Mixture-of-Experts (SMoE) router, we show that individual dynamical parameters and routing function are jointly identifiable. Across a suite of benchmarks spanning physical systems to real-world biological data, CADENCE, trained strictly on extremely sparse snapshots with context structure, matches or exceeds the performance of state-of-the-art sequential models trained on dense, full-trajectory data.

Predicting future motion is crucial in video understanding and controllable video generation. Dense point trajectories are a compact, expressive motion representation, but modeling their future evolution from observed video remains challenging. We propose a framework that predicts future trajectories and visibility from past trajectories and video context. Our method has three components: (1) Grid-Anchor Offset Encoding, which reduces location-dependent bias by representing each point as an offset from its pixel-center anchor; (2) TrajLoom-VAE, which learns a compact spatiotemporal latent space for dense trajectories with masked reconstruction and a spatiotemporal consistency regularizer; and (3) TrajLoom-Flow, which generates future trajectories in latent space via flow matching, with boundary cues and on-policy K-step fine-tuning for stable sampling. We also introduce TrajLoomBench, a unified benchmark spanning real and synthetic videos with a standardized setup aligned with video-generation benchmarks. Compared with state-of-the-art methods, our approach extends the prediction horizon from 24 to 81 frames while improving motion realism and stability across datasets. The predicted trajectories directly support downstream video generation and editing. Code, model checkpoints, and datasets are available at https://trajloom.github.io/.

In the Lagrange-Newton method, where Newton's method is applied to a Lagrangian function that includes equality constraints, all stationary points are saddle points. It is therefore not possible to use a line-search method based on the value of the objective function; instead, the line search can operate on merit functions. In this report, we explore an alternative line-search method which is applicable to this case; it particulary addresses the damping of the step length in tight valleys. We propose a line-search criterion based on the divergence of the field of Newton step vectors. The visualization of the criterion for two-dimensional test functions reveals a network of ravines with flat bottom at the zero points of the criterion. The ravines are typically connected to stationary points. To traverse this ravine network in order to approach a stationary point, a zigzag strategy is devised. Numerical experiments demonstrate that the novel line-search strategy succeeds from most starting points in all test functions, but only exhibits the desired damping of the step length in some situations. At the present stage it is therefore difficult to appraise the utility of this contribution.

Accurately predicting the future fluid is important to extensive areas, such as meteorology, oceanology and aerodynamics. However, since the fluid is usually observed from an Eulerian perspective, its active and intricate dynamics are seriously obscured and confounded in static grids, bringing horny challenges to the prediction. This paper introduces a new Lagrangian-guided paradigm to tackle the tanglesome fluid dynamics. Instead of solely predicting the future based on Eulerian observations, we propose the Eulerian-Lagrangian Dual Recurrent Network (EuLagNet), which captures multiscale fluid dynamics by tracking movements of adaptively sampled key particles on multiple scales and integrating dynamics information over time. Concretely, a EuLag Block is presented to communicate the learned Eulerian and Lagrangian features at each moment and scale, where the motion of tracked particles is inferred from Eulerian observations and their accumulated dynamics information is incorporated into Eulerian fields to guide future prediction. Tracking key particles not only provides a clear and interpretable clue for fluid dynamics but also makes our model free from modeling complex correlations among massive grids for better efficiency. Experimentally, EuLagNet excels in three challenging fluid prediction tasks, covering both 2D and 3D, simulated and real-world fluids.

A new method of analyzing grid, or aliasing, instabilities is described, in particle-in-cell (PIC) codes for plasma kinetic theory. It starts with a meshfree approach with N_{p} macroparticles, with N_{p}<infty. Linearization of these equations is done about a uniform density non-drifting equilibrium prescribed by macroparticles on a uniform lattice. Macroparticle positions perturbations are induced about this lattice. The resulting linear equations are analyzed for stability and dispersion relations. The linearized equations are then discretized on a grid of N_{g} points with N_{g} le N_{p}, in both momentum conserving (MCP) and energy conserving (ECP) formulations. For a cold stationary plasma, this leads a dynamical matrix. For ECP, the matrix is symmetric and positive definite (SPD) and immediately shows stability. For MCP, the dynamical matrix is neither symmetric nor positive definite, preventing immediate conclusions on stability. For both MCP and ECP and for a cold stationary plasma, the resulting matrix elements vary relative to the meshfree value, a result of aliasing. This deviation is periodic in the displacement of the particle lattice relative to the grid. In the MCP discretization, eigenvalues occur in complex conjugate pairs for general placement of the particle lattice relative to the grid. These conjugate pairs indicate nonnegative growth rates. The nature of the aliasing is studied and shown to be related to the trapezoidal rule error over the grid. The scaling of the linear growth rates with respect to N_{g} and especially with respect to N_{ppc} is studied. These analytical results are compared with PIC simulations and found to be in excellent agreement. The connection with a cold drifting beam is discussed briefly, specifically, grid-induced instabilities for both the MCP and ECP.

Mobile devices continuously interact with cellular base stations, generating massive volumes of signaling records that provide broad coverage for understanding human mobility. However, such records offer only coarse location cues (e.g., serving-cell identifiers) and therefore limit their direct use in applications that require high-precision GPS trajectories. This paper studies the Sig2GPS problem: reconstructing GPS trajectories from cellular signaling. Inspired by domain experts often lay the signaling trace on the map and sketch the corresponding GPS route, unlike conventional solutions that rely on complex multi-stage engineering pipelines or regress coordinates, Sig2GPS is reframed as an image-to-video generation task that directly operates in the map-visual domain: signaling traces are rendered on a map, and a video generation model is trained to draw a continuous GPS path. To support this paradigm, a paired signaling-to-trajectory video dataset is constructed to fine-tune an open-source video model, and a trajectory-aware reinforcement learning-based optimization method is introduced to improve generation fidelity via rewards. Experiments on large-scale real-world datasets show substantial improvements over strong engineered and learning-based baselines, while additional results on next GPS prediction indicate scalability and cross-city transferability. Overall, these results suggest that map-visual video generation provides a practical interface for trajectory data mining by enabling direct generation and refinement of continuous paths under map constraints.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

Stellarators offer a promising magnetic confinement approach for achieving controlled nuclear fusion. However, stellarator design remains challenging, as evaluating configuration performance requires computationally expensive, high-fidelity simulations. In particular, key performance metrics derived from guiding center simulations are costly to include directly in the design optimization loop, and are almost exclusively used as diagnostics. Machine learning has the potential to advance fusion research by enabling rapid generation and evaluation of new stellarator configurations. Effectively applying ML for fusion demands large-scale datasets that capture both design diversity and high-fidelity simulation outputs. In this work, we introduce the Benchmark of Stellarator Simulations (BoSS), a dataset of stellarator designs paired with guiding center simulation results and trajectories. The BoSS is the first large-scale dataset of guiding center simulations, containing simulation data for 180,000 distinct magnetohydrodynamic equilibria spanning a wide range of magnetic geometries and confinement properties. To exemplify the utility of ML to accelerate stellarator design, we formulate and address two sets of modeling tasks: generative modeling for designing stellarators with good particle confinement, and surrogate modeling for predicting stellarator heat deposition patterns and particle trajectories. The tasks reveal the potential impact ML can have in the stellarator field and important opportunities to improve the applicability of ML models in the sciences. Our baselines generate diverse, performant stellarators and provide useful surrogate predictions, and point to long-horizon trajectory forecasting and out-of-distribution generation as key directions for future work. The BoSS can be accessed through https://boss.flatironinstitute.org/.

The field of trajectory forecasting has grown significantly in recent years, partially owing to the release of numerous large-scale, real-world human trajectory datasets for autonomous vehicles (AVs) and pedestrian motion tracking. While such datasets have been a boon for the community, they each use custom and unique data formats and APIs, making it cumbersome for researchers to train and evaluate methods across multiple datasets. To remedy this, we present trajdata: a unified interface to multiple human trajectory datasets. At its core, trajdata provides a simple, uniform, and efficient representation and API for trajectory and map data. As a demonstration of its capabilities, in this work we conduct a comprehensive empirical evaluation of existing trajectory datasets, providing users with a rich understanding of the data underpinning much of current pedestrian and AV motion forecasting research, and proposing suggestions for future datasets from these insights. trajdata is permissively licensed (Apache 2.0) and can be accessed online at https://github.com/NVlabs/trajdata

Reinforcement learning (RL) is a powerful framework for optimizing decision-making in complex systems under uncertainty, an essential challenge in real-world settings, particularly in the context of the energy transition. A representative example is remote microgrids that supply power to communities disconnected from the main grid. Enabling the energy transition in such systems requires coordinated control of renewable sources like wind turbines, alongside fuel generators and batteries, to meet demand while minimizing fuel consumption and battery degradation under exogenous and intermittent load and wind conditions. These systems must often conform to extensive regulations and complex operational constraints. To ensure that RL agents respect these constraints, it is crucial to provide interpretable guarantees. In this paper, we introduce Shielded Controller Units (SCUs), a systematic and interpretable approach that leverages prior knowledge of system dynamics to ensure constraint satisfaction. Our shield synthesis methodology, designed for real-world deployment, decomposes the environment into a hierarchical structure where each SCU explicitly manages a subset of constraints. We demonstrate the effectiveness of SCUs on a remote microgrid optimization task with strict operational requirements. The RL agent, equipped with SCUs, achieves a 24% reduction in fuel consumption without increasing battery degradation, outperforming other baselines while satisfying all constraints. We hope SCUs contribute to the safe application of RL to the many decision-making challenges linked to the energy transition.

Model-predictive control (MPC) is a powerful tool for controlling highly dynamic robotic systems subject to complex constraints. However, MPC is computationally demanding, and is often impractical to implement on small, resource-constrained robotic platforms. We present TinyMPC, a high-speed MPC solver with a low memory footprint targeting the microcontrollers common on small robots. Our approach is based on the alternating direction method of multipliers (ADMM) and leverages the structure of the MPC problem for efficiency. We demonstrate TinyMPC's effectiveness by benchmarking against the state-of-the-art solver OSQP, achieving nearly an order of magnitude speed increase, as well as through hardware experiments on a 27 gram quadrotor, demonstrating high-speed trajectory tracking and dynamic obstacle avoidance. TinyMPC is publicly available at https://tinympc.org.

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

This paper presents methods for dramatically improving the performance of sampling-based kinodynamic planners. The key component is the first-known complete, exact steering method that produces a time-optimal trajectory between any states for a vector of synchronized double integrators. This method is applied in three ways: 1) to generate RRT edges that quickly solve the two-point boundary-value problems, 2) to produce a (quasi)metric for more accurate Voronoi bias in RRTs, and 3) to iteratively time-optimize a given collision-free trajectory. Experiments are performed for state spaces with up to 2000 dimensions, resulting in improved computed trajectories and orders of magnitude computation time improvements over using ordinary metrics and constant controls.

We present MovingParts, a NeRF-based method for dynamic scene reconstruction and part discovery. We consider motion as an important cue for identifying parts, that all particles on the same part share the common motion pattern. From the perspective of fluid simulation, existing deformation-based methods for dynamic NeRF can be seen as parameterizing the scene motion under the Eulerian view, i.e., focusing on specific locations in space through which the fluid flows as time passes. However, it is intractable to extract the motion of constituting objects or parts using the Eulerian view representation. In this work, we introduce the dual Lagrangian view and enforce representations under the Eulerian/Lagrangian views to be cycle-consistent. Under the Lagrangian view, we parameterize the scene motion by tracking the trajectory of particles on objects. The Lagrangian view makes it convenient to discover parts by factorizing the scene motion as a composition of part-level rigid motions. Experimentally, our method can achieve fast and high-quality dynamic scene reconstruction from even a single moving camera, and the induced part-based representation allows direct applications of part tracking, animation, 3D scene editing, etc.

We describe MGARD, a software providing MultiGrid Adaptive Reduction for floating-point scientific data on structured and unstructured grids. With exceptional data compression capability and precise error control, MGARD addresses a wide range of requirements, including storage reduction, high-performance I/O, and in-situ data analysis. It features a unified application programming interface (API) that seamlessly operates across diverse computing architectures. MGARD has been optimized with highly-tuned GPU kernels and efficient memory and device management mechanisms, ensuring scalable and rapid operations.

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.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for these planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.

Wasserstein gradient flow extends gradient descent to probability measures. Its Hessian-guided perturbed variant (PWGF) adds Gaussian perturbations to escape saddle points in nonconvex problems. We investigate when its approximation by finitely many interacting particles remains accurate over growing time horizons. Our analysis retains the curvature accumulated along the population-driven reference path: negative curvature can amplify approximation errors, while subsequent positive curvature can damp their influence. This captures favorable scenarios in which temporary instability is compatible with accurate tracking over growing horizons. Under regularity assumptions and a prescribed common perturbation schedule, we prove particle and objective-value tracking bounds on a high-probability event for reference paths satisfying explicit conditions on accumulated curvature. To handle state-dependent Gaussian jumps, we construct a population-first coupling that preserves the reference particles' conditional independence and reduces jump errors to covariance comparison. We verify the conditions in a variance-plus-cosine model, where curvature recovery yields a growing-horizon tracking guarantee. We also establish local attraction, transverse descent, and positive second variation in two regions of a regularized matrix-factorization model, motivating a positive-negative-positive curvature pattern.

Large language models (LLMs) encode a vast amount of world knowledge acquired from massive text datasets. Recent studies have demonstrated that LLMs can assist an embodied agent in solving complex sequential decision making tasks by providing high-level instructions. However, interactions with LLMs can be time-consuming. In many practical scenarios, they require a significant amount of storage space that can only be deployed on remote cloud server nodes. Additionally, using commercial LLMs can be costly since they may charge based on usage frequency. In this paper, we explore how to enable intelligent cost-effective interactions between the agent and an LLM. We propose When2Ask, a reinforcement learning based approach that learns when it is necessary to query LLMs for high-level instructions to accomplish a target task. Experiments on MiniGrid and Habitat environments that entail planning sub-goals demonstrate that When2Ask learns to solve target tasks with only a few necessary interactions with an LLM, and significantly reduces interaction costs in testing environments compared with baseline methods. Experiment results also suggest that by learning a mediator model to interact with the LLM, the agent's performance becomes more robust against partial observability of the environment. Our code is available at https://github.com/ZJLAB-AMMI/LLM4RL.

Understanding cellular trajectories via time-resolved single-cell transcriptomics is vital for studying development, regeneration, and disease. A key challenge is inferring continuous trajectories from discrete snapshots. Biological complexity stems from stochastic cell fate decisions, temporal proliferation changes, and spatial environmental influences. Current methods often use deterministic interpolations treating cells in isolation, failing to capture the probabilistic branching, population shifts, and niche-dependent signaling driving real biological processes. We introduce Manifold Interpolating Optimal-Transport Flow (MIOFlow) 2.0. This framework learns biologically informed cellular trajectories by integrating manifold learning, optimal transport, and neural differential equations. It models three core processes: (1) stochasticity and branching via Neural Stochastic Differential Equations; (2) non-conservative population changes using a learned growth-rate model initialized with unbalanced optimal transport; and (3) environmental influence through a joint latent space unifying gene expression with spatial features like local cell type composition and signaling. By operating in a PHATE-distance matching autoencoder latent space, MIOFlow 2.0 ensures trajectories respect the data's intrinsic geometry. Empirical comparisons show expressive trajectory learning via neural differential equations outperforms existing generative models, including simulation-free flow matching. Validated on synthetic datasets, embryoid body differentiation, and spatially resolved axolotl brain regeneration, MIOFlow 2.0 improves trajectory accuracy and reveals hidden drivers of cellular transitions, like specific signaling niches. MIOFlow 2.0 thus bridges single-cell and spatial transcriptomics to uncover tissue-scale trajectories.

Reinforcement learning fine-tuning (RLFT) is a dominant paradigm for improving pretrained policies for downstream tasks. These pretrained policies, trained on large datasets, produce generations with a broad range of promising but unrefined behaviors. Often, a critical failure mode of RLFT arises when policies lose this diversity and collapse into a handful of easily exploitable outputs. This convergence hinders exploration, which is essential for expanding the capabilities of the pretrained policy and for amplifying the benefits of test-time compute scaling. To address this, we introduce an objective for policy gradient methods that explicitly enforces the exploration and refinement of diverse generations, which we call a polychromic objective. We then show how proximal policy optimization (PPO) can be adapted to optimize this objective. Our method (1) employs vine sampling to collect on-policy rollouts and (2) modifies the advantage function to reflect the advantage under our new objective. Experiments on BabyAI, Minigrid, and Algorithmic Creativity show that our method improves success rates by reliably solving a larger set of environment configurations and generalizes better under large perturbations. Moreover, when given multiple attempts in pass@k experiments, the policy achieves substantially higher coverage, demonstrating its ability to maintain and exploit a diverse repertoire of strategies.

We propose an iterative programmatic planning (IPP) framework for solving grid-based tasks by synthesizing interpretable agent policies expressed in code using large language models (LLMs). Instead of relying on traditional search or reinforcement learning, our approach uses code generation as policy synthesis, where the LLM outputs executable programs that map environment states to action sequences. Our proposed architecture incorporates several prompting strategies, including direct code generation, pseudocode-conditioned refinement, and curriculum-based prompting, but also includes an iterative refinement mechanism that updates code based on task performance feedback. We evaluate our approach using six leading LLMs and two challenging grid-based benchmarks (GRASP and MiniGrid). Our IPP framework demonstrates improvements over direct code generation ranging from 10\% to as much as 10x across five of the six models and establishes a new state-of-the-art result for GRASP. IPP is found to significantly outperform direct elicitation of a solution from GPT-o3-mini (by 63\% on MiniGrid to 116\% on GRASP), demonstrating the viability of the overall approach. Computational costs of all code generation approaches are similar. While code generation has a higher initial prompting cost compared to direct solution elicitation (\0.08 per task vs. 0.002 per instance for GPT-o3-mini), the code can be reused for any number of instances, making the amortized cost significantly lower (by 400x on GPT-o3-mini across the complete GRASP benchmark).

Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in W_infty. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.

Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes they require. In this paper, we address this problem by decomposing the sampling process of diffusion models into two decoupled subprocesses: 1) generating a feasible trajectory, which is a time-consuming process, and 2) optimizing the trajectory. With this decomposition approach, we are able to partially separate efficiency and quality factors, enabling us to simultaneously gain efficiency advantages and ensure quality assurance. We propose the Trajectory Diffuser, which utilizes a faster autoregressive model to handle the generation of feasible trajectories while retaining the trajectory optimization process of diffusion models. This allows us to achieve more efficient planning without sacrificing capability. To evaluate the effectiveness and efficiency of the Trajectory Diffuser, we conduct experiments on the D4RL benchmarks. The results demonstrate that our method achieves it 3-it 10 times faster inference speed compared to previous sequence modeling methods, while also outperforming them in terms of overall performance. https://github.com/RenMing-Huang/TrajectoryDiffuser Keywords: Reinforcement Learning and Efficient Planning and Diffusion Model

Path-velocity decomposition is an intuitive yet powerful approach to address the complexity of kinodynamic motion planning. The difficult trajectory planning problem is solved in two separate, simpler, steps: first, find a path in the configuration space that satisfies the geometric constraints (path planning), and second, find a time-parameterization of that path satisfying the kinodynamic constraints. A fundamental requirement is that the path found in the first step should be time-parameterizable. Most existing works fulfill this requirement by enforcing quasi-static constraints in the path planning step, resulting in an important loss in completeness. We propose a method that enables path-velocity decomposition to discover truly dynamic motions, i.e. motions that are not quasi-statically executable. At the heart of the proposed method is a new algorithm -- Admissible Velocity Propagation -- which, given a path and an interval of reachable velocities at the beginning of that path, computes exactly and efficiently the interval of all the velocities the system can reach after traversing the path while respecting the system kinodynamic constraints. Combining this algorithm with usual sampling-based planners then gives rise to a family of new trajectory planners that can appropriately handle kinodynamic constraints while retaining the advantages associated with path-velocity decomposition. We demonstrate the efficiency of the proposed method on some difficult kinodynamic planning problems, where, in particular, quasi-static methods are guaranteed to fail.

We introduce transductive program synthesis, a new formulation of the program synthesis task that explicitly leverages test inputs during synthesis. While prior approaches to program synthesis--whether based on natural language descriptions or input-output examples--typically aim to generalize from training examples, they often struggle with robustness, especially in real-world settings where training examples are limited and test inputs involve various edge cases. To address this, we propose a novel framework that improves robustness by treating synthesis as an active learning over a finite hypothesis class defined by programs' outputs. We use an LLM to predict outputs for selected test inputs and eliminate inconsistent hypotheses, where the inputs are chosen via a greedy maximin algorithm to minimize the number of LLM queries required. We evaluate our approach on four benchmarks: Playgol, MBPP+, 1D-ARC, and programmatic world modeling on MiniGrid. We demonstrate that our method significantly improves program synthesis in both accuracy and efficiency. We release our code at https://github.com/klee972/SYNTRA.

Majorities of distillation methods on pre-trained diffusion models or on pre-trained rectified flow, focus on either the distillation outputs or the trajectories between random noises and clean images to speed up sample generations from pre-trained models. In those trajectory-based distillation methods, consistency distillation requires the self-consistent trajectory projection to regulate the trajectory, which might avoid the common ODE approximation error {while still be concerning about sampling efficiencies}. At the same time, rectified flow distillations enforce straight trajectory for fast sampling, although an ODE solver is still required. In this work, we propose a trajectory distillation method, \modelname, that enjoys the benefits of both and enables few-step generations. TraFlow adopts the settings of consistency trajectory models, and further enforces the properties of self-consistency and straightness throughout the entire trajectory. These two properties are pursued by reaching a balance with following three targets: (1) reconstruct the output from pre-trained models; (2) learn the amount of changes by pre-trained models; (3) satisfy the self-consistency over its trajectory. Extensive experimental results have shown the effectiveness of our proposed method.

Offline decision-making via diffusion models often produces trajectories that are misaligned with system dynamics, limiting their reliability for control. We propose Model Predictive Diffuser (MPDiffuser), a compositional diffusion framework that combines a diffusion planner with a dynamics diffusion model to generate task-aligned and dynamically plausible trajectories. MPDiffuser interleaves planner and dynamics updates during sampling, progressively correcting feasibility while preserving task intent. A lightweight ranking module then selects trajectories that best satisfy task objectives. The compositional design improves sample efficiency and adaptability by enabling the dynamics model to leverage diverse and previously unseen data independently of the planner. Empirically, we demonstrate consistent improvements over prior diffusion-based methods on unconstrained (D4RL) and constrained (DSRL) benchmarks, and validate practicality through deployment on a real quadrupedal robot.

This paper explores the problem of collision-free motion generation for manipulators by formulating it as a global motion optimization problem. We develop a parallel optimization technique to solve this problem and demonstrate its effectiveness on massively parallel GPUs. We show that combining simple optimization techniques with many parallel seeds leads to solving difficult motion generation problems within 50ms on average, 60x faster than state-of-the-art (SOTA) trajectory optimization methods. We achieve SOTA performance by combining L-BFGS step direction estimation with a novel parallel noisy line search scheme and a particle-based optimization solver. To further aid trajectory optimization, we develop a parallel geometric planner that plans within 20ms and also introduce a collision-free IK solver that can solve over 7000 queries/s. We package our contributions into a state of the art GPU accelerated motion generation library, cuRobo and release it to enrich the robotics community. Additional details are available at https://curobo.org

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

Generating interactive and dynamic 4D scenes from a single static image remains a core challenge. Most existing generate-then-reconstruct and reconstruct-then-generate methods decouple geometry from motion, causing spatiotemporal inconsistencies and poor generalization. To address these, we extend the reconstruct-then-generate framework to jointly perform Motion generation and geometric Reconstruction for 4D Synthesis (MoRe4D). We first introduce TrajScene-60K, a large-scale dataset of 60,000 video samples with dense point trajectories, addressing the scarcity of high-quality 4D scene data. Based on this, we propose a diffusion-based 4D Scene Trajectory Generator (4D-STraG) to jointly generate geometrically consistent and motion-plausible 4D point trajectories. To leverage single-view priors, we design a depth-guided motion normalization strategy and a motion-aware module for effective geometry and dynamics integration. We then propose a 4D View Synthesis Module (4D-ViSM) to render videos with arbitrary camera trajectories from 4D point track representations. Experiments show that MoRe4D generates high-quality 4D scenes with multi-view consistency and rich dynamic details from a single image. Code: https://github.com/Zhangyr2022/MoRe4D.

Most artificial life simulators either operate on abstract substrates disconnected from physical reality, or simulate physically grounded worlds that do not scale to the population sizes required for open-ended evolution. We present Microcosmos, a simulation engine in which artificial lifeforms are modeled as elastic filament chains inhabiting a two-dimensional viscous fluid world, designed from the ground up for modern GPU hardware and end-to-end differentiable simulation. We validate the engine through four experiments. Hand-designed locomotion strategies confirm that the fluid coupling respects known physical constraints. Gradient-based optimization of filament folding demonstrates both the full differentiability of the simulator and the expressivity of the filament encodings. Neuroevolution and quality-diversity search produce a wide range of swimming and chemotaxis behaviors automatically. Linear scaling with particle count confirms the engine supports large-scale simulation. Microcosmos is released as an open platform with the long-term goal of supporting large-scale open-ended evolutionary simulations, designed to be physically plausible and computationally scalable.

Autoregressive learning of time-stepping operators provides an effective approach to data-driven partial differential equation (PDE) simulation, yet for conservation laws, they face a fundamental challenge: learned updates may violate global conservation over long rollouts. For the important subclass of mass-conservation-type equations, the problem is compounded by inherent physical bounds (e.g., nonnegativity or concentrations in [0,1]) whose violation further destabilizes predictions. We introduce FluxNet, which learns cumulative transport amounts representing the total conserved quantity redistributed between each cell and a configurable neighborhood over the full surrogate interval. A conservative update guarantees exact discrete conservation by construction; modular capacity-constrained transport heads (L, U, and D) enforce lower bounds, upper bounds, or near-zero dual-bound violations through architectural design. Unlike flux-rate surrogates that require temporal integration and thus inherit CFL constraints, FluxNet involves no such integration; configurable transport neighborhoods enable large-timestep prediction at full spatial resolution. Ghost cells extend the framework to non-periodic boundaries. Experiments on four benchmarks (1D convection--diffusion, 2D shallow water, 1D traffic flow, 2D Cahn--Hilliard) demonstrate exact conservation, structural bound preservation, architecture modularity, and superior stability over flux-rate surrogates at large temporal strides. The code is publicly available at: https://github.com/Lan-zs/FluxNet.

Recent advances in diffusion-based video generation have achieved remarkable visual realism but still struggle to obey basic physical laws such as gravity, inertia, and collision. Generated objects often move inconsistently across frames, exhibit implausible dynamics, or violate physical constraints, limiting the realism and reliability of AI-generated videos. We address this gap by introducing Physical Simulator In-the-loop Video Generation (PSIVG), a novel framework that integrates a physical simulator into the video diffusion process. Starting from a template video generated by a pre-trained diffusion model, PSIVG reconstructs the 4D scene and foreground object meshes, initializes them within a physical simulator, and generates physically consistent trajectories. These simulated trajectories are then used to guide the video generator toward spatio-temporally physically coherent motion. To further improve texture consistency during object movement, we propose a Test-Time Texture Consistency Optimization (TTCO) technique that adapts text and feature embeddings based on pixel correspondences from the simulator. Comprehensive experiments demonstrate that PSIVG produces videos that better adhere to real-world physics while preserving visual quality and diversity. Project Page: https://vcai.mpi-inf.mpg.de/projects/PSIVG/

Current autoregressive diffusion models excel at video generation but are generally limited to short temporal durations. Our theoretical analysis indicates that the autoregressive modeling typically suffers from temporal drift caused by error accumulation and hinders parallelization in long video synthesis. To address these limitations, we propose a novel planning-then-populating framework centered on Macro-from-Micro Planning (MMPL) for long video generation. MMPL sketches a global storyline for the entire video through two hierarchical stages: Micro Planning and Macro Planning. Specifically, Micro Planning predicts a sparse set of future keyframes within each short video segment, offering motion and appearance priors to guide high-quality video segment generation. Macro Planning extends the in-segment keyframes planning across the entire video through an autoregressive chain of micro plans, ensuring long-term consistency across video segments. Subsequently, MMPL-based Content Populating generates all intermediate frames in parallel across segments, enabling efficient parallelization of autoregressive generation. The parallelization is further optimized by Adaptive Workload Scheduling for balanced GPU execution and accelerated autoregressive video generation. Extensive experiments confirm that our method outperforms existing long video generation models in quality and stability. Generated videos and comparison results are in our project page.

Model-predictive control (MPC) is a powerful framework for controlling dynamic systems under constraints, but it remains challenging to deploy on resource-constrained platforms, especially for problems involving conic constraints. To address this, we extend recent work developing fast, structure-exploiting, cached ADMM solvers for embedded applications, to provide support for second-order cones, as well as C++ code generation from Python, MATLAB, and Julia for easy deployment. Microcontroller benchmarks show that our solver provides up to a two-order-of-magnitude speedup, ranging from 10.6x to 142.7x, over state-of-the-art embedded solvers on QP and SOCP problems, and enables us to fit order-of-magnitude larger problems in memory. We validate our solver's deployed performance through simulation and hardware experiments, including conically-constrained trajectory tracking on a 27g Crazyflie quadrotor. To get started with Conic-TinyMPC, visit our documentation, examples, and the open-source codebase at https://tinympc.org.

Flexible robotic production requires joint decisions on process progression, material routing, resource assignment, temporary cooperation, and simultaneous execution, since each decision can affect the feasibility of the others. The challenge is greater under decentralized control, where each robot acts from bounded local information while system progress depends on collective decisions, shared resources, material state, and workspace compatibility. These properties closely match cooperative multi-agent decision making under partial observability and resource contention. This paper introduces AssemblyGrid v1, a reproducible benchmark for repeated multi-robot production that combines explicit process progression, decentralized observations, material transfer, temporary multi-robot coalitions, productive concurrency, and geometry-dependent feasibility within one task-level formulation. The benchmark includes Flow, Coalition, and Concurrency workload families, each with three scenario levels. Task success and evaluation measures are defined independently of learning reward and solution method, allowing learning-based and non-learning methods to address the same production problem. AssemblyGrid v1 is evaluated through executable conformance checks, mechanism studies, and algorithmic experiments using a privileged centralized reference, structured decentralized controllers, and MARL methods including IPPO, MAPPO, and QMIX. Results demonstrate productive execution under centralized and decentralized control. The MARL experiments further show that decentralized policies can learn effective production behavior from local observations and actions, supporting AssemblyGrid as a controlled benchmark for studying cooperative decision making in flexible robotic production.

Minibatch optimal transport coupling straightens paths in unconditional flow matching. This leads to computationally less demanding inference as fewer integration steps and less complex numerical solvers can be employed when numerically solving an ordinary differential equation at test time. However, in the conditional setting, minibatch optimal transport falls short. This is because the default optimal transport mapping disregards conditions, resulting in a conditionally skewed prior distribution during training. In contrast, at test time, we have no access to the skewed prior, and instead sample from the full, unbiased prior distribution. This gap between training and testing leads to a subpar performance. To bridge this gap, we propose conditional optimal transport C^2OT that adds a conditional weighting term in the cost matrix when computing the optimal transport assignment. Experiments demonstrate that this simple fix works with both discrete and continuous conditions in 8gaussians-to-moons, CIFAR-10, ImageNet-32x32, and ImageNet-256x256. Our method performs better overall compared to the existing baselines across different function evaluation budgets. Code is available at https://hkchengrex.github.io/C2OT

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to reduce the dimensionality of data characterized by a large Kolmogorov n-width, they typically lack a straightforward mapping from the latent space to the high-dimensional physical space. Moreover, the realized latent variables are often hard to interpret. Therefore, many of these methods are often dismissed in the reduced order modeling of dynamical systems governed by the partial differential equations (PDEs). Accordingly, we propose an auto-encoder type nonlinear dimensionality reduction algorithm. The unsupervised learning problem trains a diffeomorphic spatio-temporal grid, that registers the output sequence of the PDEs on a non-uniform parameter/time-varying grid, such that the Kolmogorov n-width of the mapped data on the learned grid is minimized. We demonstrate the efficacy and interpretability of our approach to separate convection/advection from diffusion/scaling on various manufactured and physical systems.

Reasoning about human motion is an important prerequisite to safe and socially-aware robotic navigation. As a result, multi-agent behavior prediction has become a core component of modern human-robot interactive systems, such as self-driving cars. While there exist many methods for trajectory forecasting, most do not enforce dynamic constraints and do not account for environmental information (e.g., maps). Towards this end, we present Trajectron++, a modular, graph-structured recurrent model that forecasts the trajectories of a general number of diverse agents while incorporating agent dynamics and heterogeneous data (e.g., semantic maps). Trajectron++ is designed to be tightly integrated with robotic planning and control frameworks; for example, it can produce predictions that are optionally conditioned on ego-agent motion plans. We demonstrate its performance on several challenging real-world trajectory forecasting datasets, outperforming a wide array of state-of-the-art deterministic and generative methods.

Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the B\'ezier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory (ET), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as ET space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our ET space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding ET space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed ET space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory .

Following the success of the in-context learning paradigm in large-scale language and computer vision models, the recently emerging field of in-context reinforcement learning is experiencing a rapid growth. However, its development has been held back by the lack of challenging benchmarks, as all the experiments have been carried out in simple environments and on small-scale datasets. We present XLand-100B, a large-scale dataset for in-context reinforcement learning based on the XLand-MiniGrid environment, as a first step to alleviate this problem. It contains complete learning histories for nearly 30,000 different tasks, covering 100B transitions and 2.5B episodes. It took 50,000 GPU hours to collect the dataset, which is beyond the reach of most academic labs. Along with the dataset, we provide the utilities to reproduce or expand it even further. With this substantial effort, we aim to democratize research in the rapidly growing field of in-context reinforcement learning and provide a solid foundation for further scaling. The code is open-source and available under Apache 2.0 licence at https://github.com/dunno-lab/xland-minigrid-datasets.

Computer Use Agents (CUAs) can act through both atomic GUI actions, such as click and type, and high-level tool calls, such as API-based file operations, but this hybrid action space often leaves them uncertain about when to continue with GUI actions or switch to tools, leading to suboptimal execution paths. This difficulty stems from the scarcity of high-quality interleaved GUI-Tool trajectories, the cost and brittleness of collecting real tool trajectories, and the lack of trajectory-level supervision for GUI-Tool path selection. In this paper, we propose ToolCUA, an end-to-end agent designed to learn optimal GUI-Tool path selection through a staged training paradigm. We first introduce an Interleaved GUI-Tool Trajectory Scaling Pipeline that repurposes abundant static GUI trajectories and synthesizes a grounded tool library, enabling diverse GUI-Tool trajectories without manual engineering or real tool-trajectory collection. We then perform Tool-Bootstrapped GUI RFT, combining warmup SFT with single-turn RL to improve decisions at critical GUI-Tool switching points. Finally, we optimize ToolCUA with Online Agentic RL in a high-fidelity GUI-Tool environment, guided by a Tool-Efficient Path Reward that encourages appropriate tool use and shorter execution paths. Experiments on OSWorld-MCP show that ToolCUA achieves 46.85% accuracy, a relative improvement of approximately 66% over the baseline, establishing a new state of the art among models of comparable scale. It also improves by 3.9% over GUI-only settings, demonstrating effective GUI-Tool orchestration. The results further suggest that training in a hybrid action space is a promising paradigm for real-world digital agents. Open-sourced here: https://x-plug.github.io/ToolCUA/

Controllable video generation has gained significant attention in recent years. However, two main limitations persist: Firstly, most existing works focus on either text, image, or trajectory-based control, leading to an inability to achieve fine-grained control in videos. Secondly, trajectory control research is still in its early stages, with most experiments being conducted on simple datasets like Human3.6M. This constraint limits the models' capability to process open-domain images and effectively handle complex curved trajectories. In this paper, we propose DragNUWA, an open-domain diffusion-based video generation model. To tackle the issue of insufficient control granularity in existing works, we simultaneously introduce text, image, and trajectory information to provide fine-grained control over video content from semantic, spatial, and temporal perspectives. To resolve the problem of limited open-domain trajectory control in current research, We propose trajectory modeling with three aspects: a Trajectory Sampler (TS) to enable open-domain control of arbitrary trajectories, a Multiscale Fusion (MF) to control trajectories in different granularities, and an Adaptive Training (AT) strategy to generate consistent videos following trajectories. Our experiments validate the effectiveness of DragNUWA, demonstrating its superior performance in fine-grained control in video generation. The homepage link is https://www.microsoft.com/en-us/research/project/dragnuwa/

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This conflict between generation steps and output quality arises from restrictive training objectives that focus exclusively on either infinitesimal dynamics (PF-ODEs) or direct endpoint prediction. We address this challenge by introducing an exact, continuous-time dynamics equation that analytically defines state transitions across any finite time interval. This leads to a novel generative paradigm, Transition Models (TiM), which adapt to arbitrary-step transitions, seamlessly traversing the generative trajectory from single leaps to fine-grained refinement with more steps. Despite having only 865M parameters, TiM achieves state-of-the-art performance, surpassing leading models such as SD3.5 (8B parameters) and FLUX.1 (12B parameters) across all evaluated step counts. Importantly, unlike previous few-step generators, TiM demonstrates monotonic quality improvement as the sampling budget increases. Additionally, when employing our native-resolution strategy, TiM delivers exceptional fidelity at resolutions up to 4096x4096.

Computer use agents (CUAs) have demonstrated strong capabilities in completing digital tasks. However, existing CUAs either rely solely on graphical user interface (GUI) interactions, which are often inefficient and error prone, or augment GUI interactions with application specific APIs or tools, which require substantial engineering effort and are difficult to scale across applications. We argue that the next generation of CUAs should combine GUI interactions with the command line interface (CLI), leveraging the generality of the GUI and the efficiency of shell commands. A critical challenge, however, is that current models do not know when or how to use the CLI during task execution. To address this challenge, we develop a data construction pipeline that produces three types of trajectories: GUI only, CLI only, and interleaved GUI and CLI trajectories. This pipeline results in HybridCUA-8K, containing 5K hybrid trajectories and 3K verified RLVR tasks. Building on these data, we propose a training framework with two stages: supervised fine tuning on the constructed trajectories, followed by reinforcement learning with our CLI aware rewards that encourages agents to use the CLI selectively and reliably. Experiments show that HybridCUA-9B achieves 53.6% accuracy on OSWorld, improving over the base model by 14.8 percentage points, and improves performance on WindowsAgentArena by 4.0 percentage points. These results demonstrate the effectiveness and cross platform generalizability of the hybrid GUI and CLI paradigm for computer use agents.

Effectively scaling GUI automation is essential for computer-use agents (CUAs); however, existing work primarily focuses on scaling GUI grounding rather than the more crucial GUI planning, which requires more sophisticated data collection. In reality, the exploration process of a CUA across apps/desktops/web pages typically follows a tree structure, with earlier functional entry points often being explored more frequently. Thus, organizing large-scale trajectories into tree structures can reduce data cost and streamline the data scaling of GUI planning. In this work, we propose TreeCUA to efficiently scale GUI automation with tree-structured verifiable evolution. We propose a multi-agent collaborative framework to explore the environment, verify actions, summarize trajectories, and evaluate quality to generate high-quality and scalable GUI trajectories. To improve efficiency, we devise a novel tree-based topology to store and replay duplicate exploration nodes, and design an adaptive exploration algorithm to balance the depth (i.e., trajectory difficulty) and breadth (i.e., trajectory diversity). Moreover, we develop world knowledge guidance and global memory backtracking to avoid low-quality generation. Finally, we naturally extend and propose the TreeCUA-DPO method from abundant tree node information, improving GUI planning capability by referring to the branch information of adjacent trajectories. Experimental results show that TreeCUA and TreeCUA-DPO offer significant improvements, and out-of-domain (OOD) studies further demonstrate strong generalization. All trajectory node information and code will be available at https://github.com/UITron-hub/TreeCUA.

The utilization of large-scale distributed renewable energy promotes the development of the multi-microgrid (MMG), which raises the need of developing an effective energy management method to minimize economic costs and keep self energy-sufficiency. The multi-agent deep reinforcement learning (MADRL) has been widely used for the energy management problem because of its real-time scheduling ability. However, its training requires massive energy operation data of microgrids (MGs), while gathering these data from different MGs would threaten their privacy and data security. Therefore, this paper tackles this practical yet challenging issue by proposing a federated multi-agent deep reinforcement learning (F-MADRL) algorithm via the physics-informed reward. In this algorithm, the federated learning (FL) mechanism is introduced to train the F-MADRL algorithm thus ensures the privacy and the security of data. In addition, a decentralized MMG model is built, and the energy of each participated MG is managed by an agent, which aims to minimize economic costs and keep self energy-sufficiency according to the physics-informed reward. At first, MGs individually execute the self-training based on local energy operation data to train their local agent models. Then, these local models are periodically uploaded to a server and their parameters are aggregated to build a global agent, which will be broadcasted to MGs and replace their local agents. In this way, the experience of each MG agent can be shared and the energy operation data is not explicitly transmitted, thus protecting the privacy and ensuring data security. Finally, experiments are conducted on Oak Ridge national laboratory distributed energy control communication lab microgrid (ORNL-MG) test system, and the comparisons are carried out to verify the effectiveness of introducing the FL mechanism and the outperformance of our proposed F-MADRL.

Generative sequence models are often trained to plan motion in physical domains, from robotics to mechanical simulations. When constructing a dataset to train such a model, engineers may curate demonstrations to specify how trajectories should be distributed over a physical quantity like travel distance or mechanical energy. For example, a roboticist building a maze navigation agent might choose demonstrations whose travel distances cover a fixed range uniformly, hoping to constrain the agent's expected power usage. We find that standard deep learning can violate this intent: each generated trajectory can seem plausible on its own, but the aggregate distribution over the physical quantity is wrong. We call this failure physical misgeneralization, and develop an account of its mechanism. Using controlled synthetic tasks, we show that physical misgeneralization arises when local errors typical of the model class propagate through the physical measurement to shift the recovered distribution. We estimate these errors with a data deviation kernel, and we use it to predict which physical quantities gain or lose mass in both our synthetic and more applied maze navigation and double-pendulum motion tasks. Finally, our mechanistic interpretation helps identify which mitigation strategies are structurally promising, and we use it to propose a kernel-informed intervention.

Public power-system datasets often lack electromagnetic transient (EMT) waveforms, inverter control dynamics, and diverse disturbance coverage, which limits their usefulness for training surrogate models and studying cyber-physical behavior in inverter-based microgrids. This paper presents a high-fidelity digital twin dataset generated from a MATLAB/Simulink EMT model of a low-voltage AC microgrid with ten inverter-based distributed generators. The dataset records synchronized three-phase PCC voltages and currents, per-DG active power, reactive power, and frequency, together with embedded scenario labels, producing 38 aligned channels sampled at Δt = 2~μs over T = 1~s (N = 500{,}001 samples) per scenario. Eleven operating and disturbance scenarios are included: normal operation, load step, voltage sag (temporary three-phase fault), load ramp, frequency ramp, DG trip, tie-line trip, reactive power step, single-line-to-ground faults, measurement noise injection, and communication delay. To ensure numerical stability without altering sequence length, invalid samples (NaN, Inf, and extreme outliers) are repaired using linear interpolation. Each scenario is further validated using system-level evidence from mean frequency, PCC voltage magnitude, total active power, voltage unbalance, and zero-sequence current to confirm physical observability and correct timing. The resulting dataset provides a consistent, labeled EMT benchmark for surrogate modeling, disturbance classification, robustness testing under noise and delay, and cyber-physical resilience analysis in inverter-dominated microgrids. The dataset and processing scripts will be released upon acceptance

Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that combines object particles and spatial grids in a hybrid representation. Our particle-grid model captures global shape and motion information while predicting dense particle movements, enabling the modeling of objects with varied shapes and materials. Particles represent object shapes, while the spatial grid discretizes the 3D space to ensure spatial continuity and enhance learning efficiency. Coupled with Gaussian Splattings for visual rendering, our framework achieves a fully learning-based digital twin of deformable objects and generates 3D action-conditioned videos. Through experiments, we demonstrate that our model learns the dynamics of diverse objects -- such as ropes, cloths, stuffed animals, and paper bags -- from sparse-view RGB-D recordings of robot-object interactions, while also generalizing at the category level to unseen instances. Our approach outperforms state-of-the-art learning-based and physics-based simulators, particularly in scenarios with limited camera views. Furthermore, we showcase the utility of our learned models in model-based planning, enabling goal-conditioned object manipulation across a range of tasks. The project page is available at https://kywind.github.io/pgnd .

Earthquake hazard analysis and design of spatially distributed infrastructure, such as power grids and energy pipeline networks, require scenario-specific ground-motion time histories with realistic frequency content and spatiotemporal coherence. However, producing the large ensembles needed for uncertainty quantification with physics-based simulations is computationally intensive and impractical for engineering workflows. To address this challenge, we introduce Ground-Motion Flow (GMFlow), a physics-inspired latent operator flow matching framework that generates realistic, large-scale regional ground-motion time-histories conditioned on physical parameters. Validated on simulated earthquake scenarios in the San Francisco Bay Area, GMFlow generates spatially coherent ground motion across more than 9 million grid points in seconds, achieving a 10,000-fold speedup over the simulation workflow, which opens a path toward rapid and uncertainty-aware hazard assessment for distributed infrastructure. More broadly, GMFlow advances mesh-agnostic functional generative modeling and could potentially be extended to the synthesis of large-scale spatiotemporal physical fields in diverse scientific domains.

The planning and control of a robot swarm in a complex environment have attracted increasing attention. To this end, the idea of virtual tubes has been taken up in our previous work. Specifically, a virtual tube with varying widths has been planned to avoid collisions with obstacles in a complex environment. Based on the planned virtual tube for a large number of speed-constrained robots, the average forward speed and density along the virtual tube are further planned in this paper to ensure safety and improve efficiency. Compared with the existing methods, the proposed method is based on global information and can be applied to traversing narrow spaces for speed-constrained robot swarms. Numerical simulations and experiments are conducted to show that the safety and efficiency of the passing-through process are improved. A video about simulations and experiments is available on https://youtu.be/lJHdMQMqSpc.

GUI agents require high-quality interaction trajectories to learn how software environments respond to actions, maintain state, and support multi-step workflows. However, the diversity of available trajectories is constrained by the applications, interface states, and workflows accessible in the underlying environments. Expanding this coverage requires deploying increasingly diverse and complex software, with specialized applications imposing additional installation, configuration, and runtime costs. We introduce AutoGUIWorld, a data generation framework that combines the visual priors of image generators with the task knowledge of a planner to synthesize GUI interaction trajectories without deploying or running the corresponding software environments. AutoGUIWorld samples initial GUI scenes from structured specifications of operating-system context, visual appearance, and interface state, and generates tasks conditioned on those scenes. A planner then specifies atomic actions and their intended visual consequences, while an image generator iteratively edits the current screenshot to produce subsequent observations. Action grounding and transition-level quality filtering yield 79,266 spatially annotated step-level training samples across Ubuntu, Windows, macOS, and Chrome. Fine-tuning Qwen3.5-35B-A3B on AutoGUIWorld trajectories improves the mean task score on OSWorld from 33.0% to 40.8% and the task success rate on ScienceBoard from 14.0% to 32.2%. These results show that generated trajectories improve GUI-agent performance on real desktop and scientific tasks.

Modeling and reproducing crowd behaviors are important in various domains including psychology, robotics, transport engineering and virtual environments. Conventional methods have focused on synthesizing momentary scenes, which have difficulty in replicating the continuous nature of real-world crowds. In this paper, we introduce a novel method for automatically generating continuous, realistic crowd trajectories with heterogeneous behaviors and interactions among individuals. We first design a crowd emitter model. To do this, we obtain spatial layouts from single input images, including a segmentation map, appearance map, population density map and population probability, prior to crowd generation. The emitter then continually places individuals on the timeline by assigning independent behavior characteristics such as agents' type, pace, and start/end positions using diffusion models. Next, our crowd simulator produces their long-term locomotions. To simulate diverse actions, it can augment their behaviors based on a Markov chain. As a result, our overall framework populates the scenes with heterogeneous crowd behaviors by alternating between the proposed emitter and simulator. Note that all the components in the proposed framework are user-controllable. Lastly, we propose a benchmark protocol to evaluate the realism and quality of the generated crowds in terms of the scene-level population dynamics and the individual-level trajectory accuracy. We demonstrate that our approach effectively models diverse crowd behavior patterns and generalizes well across different geographical environments. Code is publicly available at https://github.com/InhwanBae/CrowdES .

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

Classifier-free guidance (CFG) is the workhorse for steering large diffusion models toward text-conditioned targets, yet its native application to rectified flow (RF) based models provokes severe off-manifold drift, yielding visual artifacts, text misalignment, and brittle behaviour. We present Rectified-CFG++, an adaptive predictor-corrector guidance that couples the deterministic efficiency of rectified flows with a geometry-aware conditioning rule. Each inference step first executes a conditional RF update that anchors the sample near the learned transport path, then applies a weighted conditional correction that interpolates between conditional and unconditional velocity fields. We prove that the resulting velocity field is marginally consistent and that its trajectories remain within a bounded tubular neighbourhood of the data manifold, ensuring stability across a wide range of guidance strengths. Extensive experiments on large-scale text-to-image models (Flux, Stable Diffusion 3/3.5, Lumina) show that Rectified-CFG++ consistently outperforms standard CFG on benchmark datasets such as MS-COCO, LAION-Aesthetic, and T2I-CompBench. Project page: https://rectified-cfgpp.github.io/

Natural agents can effectively learn from multiple data sources that differ in size, quality, and types of measurements. We study this heterogeneity in the context of offline reinforcement learning (RL) by introducing a new, practically motivated semi-supervised setting. Here, an agent has access to two sets of trajectories: labelled trajectories containing state, action and reward triplets at every timestep, along with unlabelled trajectories that contain only state and reward information. For this setting, we develop and study a simple meta-algorithmic pipeline that learns an inverse dynamics model on the labelled data to obtain proxy-labels for the unlabelled data, followed by the use of any offline RL algorithm on the true and proxy-labelled trajectories. Empirically, we find this simple pipeline to be highly successful -- on several D4RL benchmarks~fu2020d4rl, certain offline RL algorithms can match the performance of variants trained on a fully labelled dataset even when we label only 10\% of trajectories which are highly suboptimal. To strengthen our understanding, we perform a large-scale controlled empirical study investigating the interplay of data-centric properties of the labelled and unlabelled datasets, with algorithmic design choices (e.g., choice of inverse dynamics, offline RL algorithm) to identify general trends and best practices for training RL agents on semi-supervised offline datasets.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

What data or environments to use for training to improve downstream performance is a longstanding and very topical question in reinforcement learning. In particular, Unsupervised Environment Design (UED) methods have gained recent attention as their adaptive curricula promise to enable agents to be robust to in- and out-of-distribution tasks. This work investigates how existing UED methods select training environments, focusing on task prioritisation metrics. Surprisingly, despite methods aiming to maximise regret in theory, the practical approximations do not correlate with regret but with success rate. As a result, a significant portion of an agent's experience comes from environments it has already mastered, offering little to no contribution toward enhancing its abilities. Put differently, current methods fail to predict intuitive measures of ``learnability.'' Specifically, they are unable to consistently identify those scenarios that the agent can sometimes solve, but not always. Based on our analysis, we develop a method that directly trains on scenarios with high learnability. This simple and intuitive approach outperforms existing UED methods in several binary-outcome environments, including the standard domain of Minigrid and a novel setting closely inspired by a real-world robotics problem. We further introduce a new adversarial evaluation procedure for directly measuring robustness, closely mirroring the conditional value at risk (CVaR). We open-source all our code and present visualisations of final policies here: https://github.com/amacrutherford/sampling-for-learnability.

We propose a unified, few-step generative modeling framework based on cumulative flow maps for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and cumulative parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction instantiation. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

Graphical User Interface (GUI) agents hold great potential for automating complex tasks across diverse digital environments, from web applications to desktop software. However, the development of such agents is hindered by the lack of high-quality, multi-step trajectory data required for effective training. Existing approaches rely on expensive and labor-intensive human annotation, making them unsustainable at scale. To address this challenge, we propose AgentTrek, a scalable data synthesis pipeline that generates high-quality GUI agent trajectories by leveraging web tutorials. Our method automatically gathers tutorial-like texts from the internet, transforms them into task goals with step-by-step instructions, and employs a visual-language model agent to simulate their execution in a real digital environment. A VLM-based evaluator ensures the correctness of the generated trajectories. We demonstrate that training GUI agents with these synthesized trajectories significantly improves their grounding and planning performance over the current models. Moreover, our approach is more cost-efficient compared to traditional human annotation methods. This work underscores the potential of guided replay with web tutorials as a viable strategy for large-scale GUI agent training, paving the way for more capable and autonomous digital agents.

Generative video editing has enabled several intuitive editing operations for short video clips that would previously have been difficult to achieve, especially for non-expert editors. Existing methods focus on prescribing an object's 3D or 2D motion trajectory in a video, or on altering the appearance of an object or a scene, while preserving both the video's plausibility and identity. Yet a method to move an object's 3D motion trajectory in a video, i.e., moving an object while preserving its relative 3D motion, is currently still missing. The main challenge lies in obtaining paired video data for this scenario. Previous methods typically rely on clever data generation approaches to construct plausible paired data from unpaired videos, but this approach fails if one of the videos in a pair can not easily be constructed from the other. Instead, we introduce TrajectoryAtlas, a new data generation pipeline for large-scale synthetic paired video data and a video generator TrajectoryMover fine-tuned with this data. We show that this successfully enables generative movement of object trajectories. Project page: https://chhatrekiran.github.io/trajectorymover

The field of plasma physics heavily relies on simulations to model various phenomena, such as instabilities, turbulence, and nonlinear behaviors that would otherwise be difficult to study from a purely theoretical approach. Simulations are fundamental in accurately setting up experiments, which can be extremely costly and complex. As high-fidelity tools, gyrokinetic simulations play a crucial role in discovering new physics, interpreting experimental results, and improving the design of next-generation devices. However, their high computational costs necessitate the use of acceleration platforms to reduce execution time. This work revolves around the TRIangular MEsh based Gyrokinetic (TRIMEG) code, which performs high-accuracy particle-in-cell plasma simulations in tokamak geometries, leveraging a novel finite element approach. The rise of graphical processing units (GPUs) constitutes an occasion to satisfy such computational needs, by offloading the most expensive portion of the code to the accelerators. The chosen approach features GPU offloading with the OpenMP API, which grants portability of the code to different architectures, namely AMD and NVIDIA. The particle pushing as well as the grid-to-particle operations have been ported to GPU platforms. Compiler limitations had to be overcome, and portions of the code were restructured to be suitable for GPU acceleration. Kernel performance was evaluated by carrying out GPU grid size exploration, as well as scalability studies. In addition, the efficiency of hybrid MPI-OpenMP offloading parallelization was assessed. The speedup of the GPU implementation was calculated by comparing it with the pure CPU version using different rationales. The Ion Temperature Gradient (ITG) mode was simulated using the GPU-accelerated version, and its correctness was verified in terms of the energy growth rate and the two-dimensional mode structures.

Modeling wind-driven object dynamics from video observations is highly challenging due to the invisibility and spatio-temporal variability of wind, as well as the complex deformations of objects. We present DiffWind, a physics-informed differentiable framework that unifies wind-object interaction modeling, video-based reconstruction, and forward simulation. Specifically, we represent wind as a grid-based physical field and objects as particle systems derived from 3D Gaussian Splatting, with their interaction modeled by the Material Point Method (MPM). To recover wind-driven object dynamics, we introduce a reconstruction framework that jointly optimizes the spatio-temporal wind force field and object motion through differentiable rendering and simulation. To ensure physical validity, we incorporate the Lattice Boltzmann Method (LBM) as a physics-informed constraint, enforcing compliance with fluid dynamics laws. Beyond reconstruction, our method naturally supports forward simulation under novel wind conditions and enables new applications such as wind retargeting. We further introduce WD-Objects, a dataset of synthetic and real-world wind-driven scenes. Extensive experiments demonstrate that our method significantly outperforms prior dynamic scene modeling approaches in both reconstruction accuracy and simulation fidelity, opening a new avenue for video-based wind-object interaction modeling.

Visual generation has witnessed remarkable progress in single-image tasks, yet extending these capabilities to temporal sequences remains challenging. Current approaches either build specialized video models from scratch with enormous computational costs or add separate motion modules to image generators, both requiring learning temporal dynamics anew. We observe that modern image generation models possess underutilized potential in handling structured layouts with implicit temporal understanding. Building on this insight, we introduce GRID, which reformulates temporal sequences as grid layouts, enabling holistic processing of visual sequences while leveraging existing model capabilities. Through a parallel flow-matching training strategy with coarse-to-fine scheduling, our approach achieves up to 67 faster inference speeds while using <1/1000 of the computational resources compared to specialized models. Extensive experiments demonstrate that GRID not only excels in temporal tasks from Text-to-Video to 3D Editing but also preserves strong performance in image generation, establishing itself as an efficient and versatile omni-solution for visual generation.

We develop a learning-based framework for constructing shrinking disturbance-invariant tubes under state- and input-dependent uncertainty, intended as a building block for tube Model Predictive Control (MPC), and certify safety via a lifted, isotone (order-preserving) fixed-point map. Gaussian Process (GP) posteriors become (1-α) credible ellipsoids, then polytopic outer sets for deterministic set operations. A two-time-scale scheme separates learning epochs, where these polytopes are frozen, from an inner, outside-in iteration that converges to a compact fixed point Z^star!subseteq!mathcal G; its state projection is RPI for the plant. As data accumulate, disturbance polytopes tighten, and the associated tubes nest monotonically, resolving the circular dependence between the set to be verified and the disturbance model while preserving hard constraints. A double-integrator study illustrates shrinking tube cross-sections in data-rich regions while maintaining invariance.

Machine-learning surrogates are increasingly used to accelerate computational fluid dynamics, yet progress is limited by the lack of benchmarks capturing realistic, time-dependent turbulent flows. We introduce TurtLES, a 14 TB dataset of 3D turbulent cylinder wakes in the shear-layer transition regime, computed via high-fidelity implicit large-eddy simulations. The dataset contains 400 trajectories of 400 time steps each, with 3-11 million points per frame, spanning variations in geometry, Reynolds number, and angle of attack. Unlike existing datasets, TurtLES combines (i) physically realistic turbulence with an active energy cascade driven by vortex stretching, (ii) dense irregular meshes, and (iii) long-horizon temporal dynamics. We benchmark state-of-the-art neural operators on autoregressive rollouts and identify key failure modes, including temporal instability, loss of small-scale energy, and challenges in learning on large irregular domains. TurtLES provides a new benchmark for evaluating surrogate models on 3D turbulent wakes at industrially relevant mesh resolution.

Drones equipped with cameras are emerging as a powerful tool for large-scale aerial 3D scanning, but existing automatic flight planners do not exploit all available information about the scene, and can therefore produce inaccurate and incomplete 3D models. We present an automatic method to generate drone trajectories, such that the imagery acquired during the flight will later produce a high-fidelity 3D model. Our method uses a coarse estimate of the scene geometry to plan camera trajectories that: (1) cover the scene as thoroughly as possible; (2) encourage observations of scene geometry from a diverse set of viewing angles; (3) avoid obstacles; and (4) respect a user-specified flight time budget. Our method relies on a mathematical model of scene coverage that exhibits an intuitive diminishing returns property known as submodularity. We leverage this property extensively to design a trajectory planning algorithm that reasons globally about the non-additive coverage reward obtained across a trajectory, jointly with the cost of traveling between views. We evaluate our method by using it to scan three large outdoor scenes, and we perform a quantitative evaluation using a photorealistic video game simulator.

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE's flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.

This paper presents a continuous-time optimal control framework for the generation of reference trajectories in driving scenarios with uncertainty. A previous work presented a discrete-time stochastic generator for autonomous vehicles; those results are extended to continuous time to ensure the robustness of the generator in a real-time setting. We show that the stochastic model in continuous time can capture the uncertainty of information by producing better results, limiting the risk of violating the problem's constraints compared to a discrete approach. Dynamic solvers provide faster computation and the continuous-time model is more robust to a wider variety of driving scenarios than the discrete-time model, as it can handle further time horizons, which allows trajectory planning outside the framework of urban driving scenarios.

In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a "lazy" dynamic programming recursion on a predetermined number of probabilistically-drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds--the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order O(n^{-1/d+ρ}), where n is the number of sampled points, d is the dimension of the configuration space, and ρ is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive.

Single-cell snapshot data can resolve a continuum of cellular states but do not uniquely determine the dynamics governing transitions between them. However, additional dynamical information can often be encoded in a cell-cell Markov transition kernel. Existing generative approaches for single cell trajectory inference either infer transport only from population marginals, impose a symmetric geometry on the state space, or incorporate directionality through a single velocity vector at each observed state. We introduce Finsler Flow Matching (FFM), a framework for learning continuous stochastic dynamics from discrete Markov transition graphs. We use the first and second local moments to construct a Finsler structure motivated by the Freidlin--Wentzell action, where the second moment determines anisotropic accessibility and the first moment introduces a preferred direction of motion. We learn neural approximations of the resulting directed geodesics, use their Finsler cost to construct source-target couplings, and define geometry-aware stochastic conditional paths that can be distilled into a continuous generative process through simulation-free score and flow matching. Across synthetic and single-cell trajectory inference benchmarks, FFM improves recovery of withheld intermediate populations, particularly when the transition dynamics are strongly directional or anisotropic. Our results provide a principled route from discrete transition probabilities to continuous generative dynamics while retaining both directional and diffusive structure.

Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.

Video generation models have shown strong potential as world models for autonomous driving simulation. However, existing approaches are primarily trained on real-world driving datasets, which mostly contain natural and safe driving scenarios. As a result, current models often fail when conditioned on challenging or counterfactual trajectories-such as imperfect trajectories generated by simulators or planning systems-producing videos with severe physical inconsistencies and artifacts. To address this limitation, we propose PhyGenesis, a world model designed to generate driving videos with high visual fidelity and strong physical consistency. Our framework consists of two key components: (1) a physical condition generator that transforms potentially invalid trajectory inputs into physically plausible conditions, and (2) a physics-enhanced video generator that produces high-fidelity multi-view driving videos under these conditions. To effectively train these components, we construct a large-scale, physics-rich heterogeneous dataset. Specifically, in addition to real-world driving videos, we generate diverse challenging driving scenarios using the CARLA simulator, from which we derive supervision signals that guide the model to learn physically grounded dynamics under extreme conditions. This challenging-trajectory learning strategy enables trajectory correction and promotes physically consistent video generation. Extensive experiments demonstrate that PhyGenesis consistently outperforms state-of-the-art methods, especially on challenging trajectories. Our project page is available at: https://wm-research.github.io/PhyGenesis/.

We delve into the physics-informed neural reconstruction of smoke and obstacles through sparse-view RGB videos, tackling challenges arising from limited observation of complex dynamics. Existing physics-informed neural networks often emphasize short-term physics constraints, leaving the proper preservation of long-term conservation less explored. We introduce Neural Characteristic Trajectory Fields, a novel representation utilizing Eulerian neural fields to implicitly model Lagrangian fluid trajectories. This topology-free, auto-differentiable representation facilitates efficient flow map calculations between arbitrary frames as well as efficient velocity extraction via auto-differentiation. Consequently, it enables end-to-end supervision covering long-term conservation and short-term physics priors. Building on the representation, we propose physics-informed trajectory learning and integration into NeRF-based scene reconstruction. We enable advanced obstacle handling through self-supervised scene decomposition and seamless integrated boundary constraints. Our results showcase the ability to overcome challenges like occlusion uncertainty, density-color ambiguity, and static-dynamic entanglements. Code and sample tests are at https://github.com/19reborn/PICT_smoke.

Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.