Daily Papers

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

We present a novel approach to determine the constitutive properties of metals under large plastic strains and strain rates that otherwise are difficult to access using conventional materials testing methods. The approach exploits large-strain plastic flow past a sharp wedge, coupled with high-speed photography and image velocimetry to capture the underlying plastic flow dynamics. The inverse problem of estimating material parameters from the flow field is solved using an iterative optimization procedure that minimizes the gap between internal and external plastic work. A major advantage of the method is that it neither makes any assumptions about the flow nor requires computational simulations. To counter the problem of non-unique parameter estimates, we propose a parameterization scheme that takes advantage of the functional form of the constitutive model and reformulates the problem into a more tractable form to identify plasticity parameters uniquely. We present studies to illustrate the principle of the method with two materials with widely different plastic flow characteristics: copper (strain hardening) and a lead-free solder alloy (rate sensitive and deformation history dependent). The results demonstrate the efficacy of the method in reliably determining the material parameters under high strain/strain rate conditions of relevance to a range of practical engineering problems.

Large language model (LLM)-based agentic frameworks increasingly adopt the paradigm of dynamically generating task-specific agents. We suggest that not only agents but also specialized software modules for scientific and engineering tasks can be generated on demand. We demonstrate this concept in the field of solid mechanics. There, so-called constitutive models are required to describe the relationship between mechanical stress and body deformation. Constitutive models are essential for both the scientific understanding and industrial application of materials. However, even recent data-driven methods of constitutive modeling, such as constitutive artificial neural networks (CANNs), still require substantial expert knowledge and human labor. We present a framework in which an LLM generates a CANN on demand, tailored to a given material class and dataset provided by the user. The framework covers LLM-based architecture selection, integration of physical constraints, and complete code generation. Evaluation on three benchmark problems demonstrates that LLM-generated CANNs achieve accuracy comparable to or greater than manually engineered counterparts, while also exhibiting reliable generalization to unseen loading scenarios and extrapolation to large deformations. These findings indicate that LLM-based generation of physics-constrained neural networks can substantially reduce the expertise required for constitutive modeling and represent a step toward practical end-to-end automation.

The aim of the present work is to investigate the influence of the realistic model parameters on the equipartition of energy in a vibrofluidized system. To achieve this, a three-dimensional vertically vibrated granular system consisting of spherical particles is simulated using the discrete element method (DEM) using the open-source software LAMMPS. Interparticle and wall-particle interactions are determined using the linear-spring dashpot model. Simulations are performed for nearly perfectly smooth to nearly perfectly rough particles. Two different values for the ratio of the tangential to normal spring stiffness coefficient kappa (2/7 and 3/4) are chosen. Non-equipartition of energy between the translational and rotational modes is observed for all realistic values in the parametric range.

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

Modelling physical systems with partial differential equations (PDEs) is central to science and engineering, yet in most real applications the PDE model is incomplete: relationships such as constitutive or thermal laws are unknown. Existing surrogate approaches close this gap by learning the PDE solution from data, but remain tied to a specific configuration (geometry, boundary conditions, discretisation) and recover the solution rather than the missing physics itself. We introduce FEML, an end-to-end differentiable framework that couples the known PDE with a machine-learned operator for the missing physics. Embedding the PDE solver into training lets this operator be learned directly from the PDE solution, even when its own output cannot be measured - for example, stress in constitutive laws. Because the operator is independent of the system configuration, a law learned in one setting transfers zero-shot to new geometries, boundary conditions, and discretisations, and can be inspected by domain specialists. FEML represents the operator with structure-preserving operator networks (SPONs), which retain key continuous properties at the discrete level. We demonstrate FEML across solid mechanics and thermal transport. From synthetic data we progressively discover an elastoplastic law - the nonlinear elastic response, then the plastic hardening law - and compose them into a foundation constitutive model that transfers zero-shot to a 3D torsion problem. Moving to real data, we learn coupled plastic-hardening and ductile-damage laws from a benchmark shear-coupon test, reproducing the measured response, including post-peak softening, to within the experimental scatter. Finally, we recover a temperature-dependent conductivity from transient heat-flow data and apply symbolic regression to the learned operator to extract a closed-form law matching the ground truth.

This study proposes a modularized deep learning-based loading protocol for optimal parameter estimation of Bouc-Wen (BW) class models. The protocol consists of two key components: optimal loading history construction and CNN-based rapid parameter estimation. Each component is decomposed into independent sub-modules tailored to distinct hysteretic behaviors-basic hysteresis, structural degradation, and pinching effect-making the protocol adaptable to diverse hysteresis models. Three independent CNN architectures are developed to capture the path-dependent nature of these hysteretic behaviors. By training these CNN architectures on diverse loading histories, minimal loading sequences, termed loading history modules, are identified and then combined to construct an optimal loading history. The three CNN models, trained on the respective loading history modules, serve as rapid parameter estimators. Numerical evaluation of the protocol, including nonlinear time history analysis of a 3-story steel moment frame and fragility curve construction for a 3-story reinforced concrete frame, demonstrates that the proposed protocol significantly reduces total analysis time while maintaining or improving estimation accuracy. The proposed protocol can be extended to other hysteresis models, suggesting a systematic approach for identifying general hysteresis models.

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

We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a kinematic constraint, the force-balance equations are derived using variational principles, with the pressure--density constitutive relation emerging as a direct consequence of the variational structure; the same kinematic constraint also supplies the total-flux transport structure. In the ideal-gas limit, the model linearization recovers the classical linear Biot equations. For power-law fluid energies, it yields isentropic pressure--density relations. A key advantage of the variational formulation is that extensions to richer physics, such as thermal effects, chemical reactions, or multi-component fluids, can be incorporated systematically by augmenting the energy and dissipation functionals without redesigning the force-balance or transport closure. We support the model with an energy-compatible two-field discretization and study consolidation under a surface load with three lateral-boundary treatments and three fluid-compressibility exponents.

Layered viscoelastic interiors control the frequency dependence of planetary tidal dissipation, but repeated layered Love-number calculations are expensive in long-term orbital and spin integrations. Equivalent homogeneous rheologies provide a cheaper representation of the same response, but their effective parameters do not by themselves identify the interior layers they represent. We develop a local interpretation of such parameters by differentiating the layered-to-homogeneous construction about a fixed-geometry baseline, perturbing only selected layer rigidities and viscosities. We use the pole-residue representation of the degree-two Love number to construct a physical-to-effective transfer matrix. We then use its singular values, resolution matrix, and mode-dominance matrix to determine which physical perturbations are visible in the Love-number response and how they appear in effective-rheology coordinates. Applied to a five-layer lunar model, the full degree-two response is sensitive to seven of eight solid-layer rheological parameters. The single near-null direction is the inner-core rigidity, consistent with shielding by the fluid outer core and with the weak dependence of Love numbers on core elastic structure. Over the LLR frequency interval, fewer physical directions are visible. To first order, the elastic spring, isolated dashpot, and two Voigt elements reproduce the nine-pole response over this interval. Finite perturbations confirm the tangent prediction to within a few percent, with the validity radius limited by a nearly degenerate pair of long-timescale modes.

The intrinsic dynamics of an object governs its physical behavior in the real world, playing a critical role in enabling physically plausible interactive simulation with 3D assets. Existing methods have attempted to infer the intrinsic dynamics of objects from visual observations, but generally face two major challenges: one line of work relies on manually defined constitutive priors, making it difficult to generalize to complex scenarios; the other models intrinsic dynamics using neural networks, resulting in limited interpretability and poor generalization. To address these challenges, we propose VisionLaw, a bilevel optimization framework that infers interpretable expressions of intrinsic dynamics from visual observations. At the upper level, we introduce an LLMs-driven decoupled constitutive evolution strategy, where LLMs are prompted as a knowledgeable physics expert to generate and revise constitutive laws, with a built-in decoupling mechanism that substantially reduces the search complexity of LLMs. At the lower level, we introduce a vision-guided constitutive evaluation mechanism, which utilizes visual simulation to evaluate the consistency between the generated constitutive law and the underlying intrinsic dynamics, thereby guiding the upper-level evolution. Experiments on both synthetic and real-world datasets demonstrate that VisionLaw can effectively infer interpretable intrinsic dynamics from visual observations. It significantly outperforms existing state-of-the-art methods and exhibits strong generalization for interactive simulation in novel scenarios.

In this work, we propose a framework that constructs reduced order models for nonlinear structural mechanics in a nonintrusive fashion, and can handle large scale simulations. We identify three steps that are carried out separately in time, and possibly on different devices: (i) the production of high-fidelity solutions by a commercial software, (ii) the offline stage of the model reduction and (iii) the online stage where the reduced order model is exploited. The nonintrusivity assumes that only the displacement field solution is known, and relies on operations on simulation data during the offline phase by using an in-house code. The compatibility with a new commercial code only needs the implementation of a routine converting the mesh and result format into our in-house data format. The nonintrusive capabilities of the framework are demonstrated on numerical experiments using commercial versions of the finite element softwares Zset and Ansys Mechanical. The nonlinear constitutive equations are evaluated by using the same external plugins as for Zset or Ansys Mechanical. The large scale simulations are handled using domain decomposition and parallel computing with distributed memory. The features and performances of the framework are evaluated on two numerical applications involving elastoviscoplastic materials: the second one involves a model of high-pressure blade, where the framework is used to extrapolate cyclic loadings in 6.5 hours, whereas the reference high-fidelity computation would take 9.5 days.

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

Nonlinear elastic properties of polymers and polymeric composites are essential for accurate prediction of their response to dynamic loads, which is crucial in a wide range of applications. These properties can be affected by strain rate, temperature, and pressure. The temperature susceptibility of nonlinear elastic moduli of polymers remains poorly understood. We have recently observed a significant frequency dependence of the nonlinear elastic (Murnaghan) moduli of polystyrene. In this paper we expand this analysis by the temperature dependence. The measurement methodology was based on the acousto-elastic effect, and involved analysis of the dependencies of velocities of longitudinal and shear single-frequency ultrasonic waves in the sample on the applied static pressure. Measurements were performed at different temperatures in the range of 25-65 {\deg}C and at different frequencies in the range of 0.75-3 MHz. The temperature susceptibility of the nonlinear moduli l and m was found to be two orders of magnitude larger than that of linear moduli lambda and mu. At the same time, the observed variations of n modulus with temperature were low and within the measurement tolerance. The observed tendencies can be explained by different influence of pressure on relaxation processes in the material at different temperatures.

Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, e.g., uncertainty quantification, remeshing applications, topology optimization, and so forth. This limitation has motivated the application of data-driven surrogate models, where the microscale computations are substituted with a surrogate, usually acting as a black-box mapping between macroscale quantities. These models offer significant speedups but struggle with incorporating microscale physical constraints, such as the balance of linear momentum and constitutive models. In this contribution, we propose Equilibrium Neural Operator (EquiNO) as a complementary physics-informed PDE surrogate for predicting microscale physics and compare it with variational physics-informed neural and operator networks. Our framework, applicable to the so-called multiscale FE^{,2}, computations, introduces the FE-OL approach by integrating the finite element (FE) method with operator learning (OL). We apply the proposed FE-OL approach to quasi-static problems of solid mechanics. The results demonstrate that FE-OL can yield accurate solutions even when confronted with a restricted dataset during model development. Our results show that EquiNO achieves speedup factors exceeding 8000-fold compared to traditional methods and offers an optimal balance between data-driven and physics-based strategies.

In this paper, we introduce tensor involved peridynamics, a unified framework for simulating both isotropic and anisotropic materials. While traditional peridynamics models effectively simulate isotropic materials, they face challenges with anisotropic materials and are prone to instability caused by zero energy modes. Our novel model extend the linear bond based peridynamics framework by incorporating the elastic tensor into the micrmodulus function, thereby ensuring stability for anisotropic materials without the need for additional corrections. For isotropic materials. the model mantains compatibility with conventional bond based peridynamics, assuming Possion's rations of 1/4 in 3D and 1/3 in 2D.Numerical experiments confirm the model's stability and accuracy across various scenarios. Additionally, we introduce a damage model for isotropic materials. validating its performance in predicting crack propagation paths in a 2D plate. The results show superior alignment with experimental date compared to traditional model.

We consider the matrix composite materials (CM) of either random (statistically homogeneous or inhomogeneous), periodic, or deterministic (neither random nor periodic) structures. CMs exhibit linear or nonlinear behavior, coupled or uncoupled multi-physical phenomena, locally elastic, weakly nonlocal (strain gradient and stress gradient), or strongly nonlocal (strain-type and displacement-type, peridynamics) phase properties. A modified Computational Analytical Micromechanics (CAM) approach introduces an exact Additive General Integral Equation (AGIE) for CMs of any structure and phase properties mentioned above. The unified iteration solution of static AGIEs is adapted to the body force with compact support serving as a fundamentally new universal training parameter. The approach also establishes a critical threshold for filtering out unsuitable sub-datasets of effective parameters through a novel Representative Volume Element (RVE) concept, which extends Hill's classical framework. This RVE concept eliminates sample size, boundary layer, and edge effects, making it applicable to CMs of any structure and phase properties, regardless of local or nonlocal, linear or nonlinear. Incorporating this new RVE concept into machine learning and neural network techniques enables the construction of any unpredefined surrogate nonlocal operators. The methodology is structured as a modular, block-based framework, allowing independent development and refinement of software components. This flexible, robust AGIE-CAM framework integrates data-driven, multi-scale, and multi-physics modeling, accelerating research in CM of any microtopology and phase properties considered. The AGIE-CAM framework represents a groundbreaking paradigm shift in the micromechanics of composites, redefining the very philosophy that underpins our understanding of their behavior at the microscopic level.

In detuned optical cavities, the radiation pressure force acting on the mirrors depends on their displacements. This is equivalent to the rigidity (the optical spring), inserted between the mirrors. This effect can be used for optimization of the mechanical susceptibility of probe mirrors in high-precision force sensors. However, in some cases, the use of detuned cavities or even just any high-finesse cavities could be problematic due to technological constraints. We consider a new type of the optical spring that does not require the cavity (but can use a resonance tuned one to increase the optomechanical coupling). Instead, it uses the double interaction of the probing light with the mechanical object. We propose two possible implementation of this concept, suitable, respectively, for the atomic spin ensembles and for the laser gravitational-wave detectors.

In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights. The correspondence is exact for log-sum-exp layers and structural for broader architectures: residual networks, transformers, and recurrent architectures (RNNs, LSTMs, SSMs) each discretize the same class of Hamilton--Jacobi equations, with architecture-dependent Hamiltonian and viscosity. A single deformation parameter varepsilon unifies all four perspectives (network, tropical algebra, viscous PDE, convex optimization) in a commutative diagram closed under Lipschitz conditions. Quantitative consequences include: the minimax optimal generalization rate O(n^{-1/(d+2)}) for fixed t; adversarial robustness controlled by varepsilon; backpropagation as the co-state equation of the Hamiltonian system for residual networks (Pontryagin Maximum Principle); scaling exponents consistent with data intrinsic dimension via PDE quadrature; and a closed-form O(N) influence function (softmax attribution weights π_j) whose entropy landscape undergoes fold bifurcations as varepsilon increases, each merging attribution basins.

Pressure, together with temperature and magnetic field, is an important thermodynamical parameter in physics. Investigating the response of a compound or of a material to pressure allows to elucidate ground states, investigate their interplay and interactions and determine microscopic parameters. Pressure tuning is used to establish phase diagrams, study phase transitions and identify critical points. Muon spin rotation/relaxation (muSR) is now a standard technique making increasing significant contribution in condensed matter physics, material science research and other fields. In this review, we will discuss specific requirements and challenges to perform muSR experiments under pressure, introduce the high-pressure muon facility at the Paul Scherrer Institute (PSI, Switzerland) and present selected results obtained by combining the sensitivity of the muSR technique with pressure.

Compliance is a useful parametrization of tactile information that humans often utilize in manipulation tasks. It can be used to inform low-level contact-rich actions or characterize objects at a high-level. In robotic manipulation, existing approaches to estimate compliance have struggled to generalize across object shape and material. Using camera-based tactile sensors, we present a novel approach to parametrize compliance through Young's modulus E. We evaluate our method over a novel dataset of 285 common objects, including a wide array of shapes and materials with Young's moduli ranging from 5.0 kPa to 250 GPa. Data is collected over automated parallel grasps of each object. Combining analytical and data-driven approaches, we develop a hybrid system using a multi-tower neural network to analyze a sequence of tactile images from grasping. This system is shown to estimate the Young's modulus of unseen objects within an order of magnitude at 74.2% accuracy across our dataset. This is a drastic improvement over a purely analytical baseline, which exhibits only 28.9% accuracy. Importantly, this estimation system performs irrespective of object geometry and demonstrates robustness across object materials. Thus, it could be applied in a general robotic manipulation setting to characterize unknown objects and inform decision-making, for instance to sort produce by ripeness.

Data-driven surrogate models are an alternative to numerical homogenization of heterogeneous materials. In this contribution, a supervised learning approach is presented for predicting effective Lamé parameters of hyperelastic composites from low-dimensional microstructural descriptors. The data set is based on previously published numerical homogenization results for ensembles of two-phase stochastic microstructures generated by planar Boolean models, covering variations of inclusion shape, phase contrast, and area fraction; see Brändel, Brands, Maike, Rheinbach, Schröder, Schwarz and Stoyan (2022). A neural network is trained on combinations of scalar and curve-valued statistical descriptors, including the area fraction, a derived scalar shape descriptor τ, the two-point correlation function S_2(r), and the lineal-path function ell(z). Additional data representing limiting cases of the parameter space are incorporated to stabilize training and improve extrapolation behavior. The surrogate is evaluated by leave-one-grain-type-out cross-validation in order to assess generalization to unseen grain geometries. Numerical results demonstrate that additional descriptors can reduce relative errors. A predictor trained with τ and S_2(r) provides a compact representation with good quantitative accuracy and regular dense response behavior. Adding the lineal-path function ell(z) further reduces the error at the available data points, indicating that it is a promising additional descriptor; however, dense post-training response evaluations show that improved pointwise accuracy does not automatically guarantee physically admissible behavior between sampled parameter values. This motivates future work on physically constrained surrogate models, loss formulations, bounded output parametrizations, and a more systematic representation of curve-valued geometric descriptors.

The industrial application motivating this work is the fatigue computation of aircraft engines' high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes {the classical unenriched proper orthogonal decomposition method} fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the {error indicator} becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving 5 million degrees of freedom, where the whole procedure is computed in parallel with distributed memory.

This work develops a theoretical model for steady thermodynamic and kinematic profiles for severe convective storm environments, building off of the two-layer static energy framework developed in Agard and Emanuel (2017). The model is phrased in terms of static energy, and it allows for independent variation of the boundary layer and free troposphere separated by a capping inversion. An algorithm is presented to apply the model to generate a sounding for numerical simulations of severe convective storms, and the model is compared and contrasted with that of Weisman and Klemp. The model is then fit to a case-study sounding associated with the 3 May 1999 tornado outbreak, and its potential utility is demonstrated via idealized numerical simulation experiments. A long-lived supercell is successfully simulated with the historical sounding but not the analogous theoretical sounding. Two types of example experiments are then performed that do simulate a long-lived supercell: 1) a semi-theoretical experiment in which a portion of the theoretical sounding is modified to match the real sounding (low-level moisture); 2) a fully-theoretical experiment in which a model physical parameter is modified (free-tropospheric relative humidity). Overall, the construction of this minimal model is flexible and amenable to additional modifications as needed. The model offers a novel framework that may be useful for testing how severe convective storms depend on the vertical structure of the hydrostatic environment, as well as for linking variability in these environments to the physical processes that produce them within the climate system.

The Gauge-Including Projector Augmented Wave (GIPAW) method, within the Density Functional Theory (DFT) Generalized Gradient Approximation (GGA) framework, is applied to compute solid state NMR parameters for ^{27}Al in the α, θ, and κ aluminium oxide phases and their gibbsite and boehmite precursors. The results for well-established crystalline phases compare very well with available experimental data and provide confidence in the accuracy of the method. For γ-alumina, four structural models proposed in the literature are discussed in terms of their ability to reproduce the experimental spectra also reported in the literature. Among the considered models, the Fd3m structure proposed by Paglia {\it et al.} [Phys. Rev. B {\bf 71}, 224115 (2005)] shows the best agreement. We attempt to link the theoretical NMR parameters to the local geometry. Chemical shifts depend on coordination number but no further correlation is found with geometrical parameters. Instead our calculations reveal that, within a given coordination number, a linear correlation exists between chemical shifts and Born effective charges.

We analyse the boundary behaviour of the gradient of the torsion function w_Om in convex domains OmsubsetR^d. We prove that its L^infty-norm is attained at a boundary point and establish the stability of this norm under general (convex) perturbations. For problems of the form $sup{|nabla w_{Om}|_infty: Om subset R^d,open, bounded and convex, G(Om)=m}, where G is either volume or perimeter, we show the existence of maximisers which are C^1-smooth, rotationally symmetric about an axis and contain a (d-1)$- dimensional ball (of estimated size) in their boundary. Other constraints, whether geometric (such as diameter or circumradius) or variational (such as torsion or first Dirichlet eigenvalue), are also briefly discussed, and some of their characteristic behaviours are highlighted.

Purpose: Six million people use crutches as mobile aids in the US. Rigid designs with no axial mobility limit sensory feedback and lead to secondary injury on the upper joints. Spring-loaded designs offer compliance but may compromise stability. We designed a biologically inspired tensegrity crutch with a compliant module aiming to achieve favorable mechanical properties. The terminal module was a pre-stressed self-tensile two-cell tensegrity structure. We compared the tensegrity crutch to commercial rigid and spring-loaded crutches in mechanical tests using axial loading, in overground straight and turning walking, and in participant experience. Methods: In human trials, healthy young adults (N=18) with no recent lower-body injury performed straight walking and turning trials at a comfortable self-selected pace. A knee blocker simulated unilateral injury of the dominant leg. After using each type of crutch, participants reported their perceived levels of effort, comfort, pain, stability, and usability. Results: Compared to the rigid design, both spring-loaded and tensegrity conditions reduced peak loading rates. The tensegrity design improved effort, comfort, pain, and usability. Spring-loaded crutches reduced perceived stability and walking speed. Conclusion: The biologically inspired tensegrity crutches were an overall improvement to existing designs. Simulations and mechanical testing suggest that nonlinear stiffness, ground-following, and force feedback are among the beneficial mechanical properties that underlie this improvement.

Accurate grasp force control is one of the key skills for ensuring successful and damage-free robotic grasping of objects. Although existing methods have conducted in-depth research on slip detection and grasping force planning, they often overlook the issue of adaptive tracking of the actual force to the target force when handling objects with different material properties. The optimal parameters of a force tracking controller are significantly influenced by the object's stiffness, and many adaptive force tracking algorithms rely on stiffness estimation. However, real-world objects often exhibit viscous, plastic, or other more complex nonlinear time-varying behaviors, and existing studies provide insufficient support for these materials in terms of stiffness definition and estimation. To address this, this paper introduces the concept of generalized stiffness, extending the definition of stiffness to nonlinear time-varying grasp system models, and proposes an online generalized stiffness estimator based on Long Short-Term Memory (LSTM) networks. Based on generalized stiffness, this paper proposes an adaptive parameter adjustment strategy using a PI controller as an example, enabling dynamic force tracking for objects with varying characteristics. Experimental results demonstrate that the proposed method achieves high precision and short probing time, while showing better adaptability to non-ideal objects compared to existing methods. The method effectively solves the problem of grasp force tracking in unknown, nonlinear, and time-varying grasp systems, demonstrating the generalization capability of our neural network and enhancing the robotic grasping ability in unstructured environments.

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and accurate multi-physics computational models are computationally expensive and their personalisation involves fine calibration of a large number of parameters, which may be space-dependent, challenging their clinical translation. In this work, we propose a new approach which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models, capable of reconstructing displacement fields and estimating heterogeneous patient-specific biophysical properties. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting, and combines it with the physics of the problem, represented by a mathematical model based on partial differential equations, to regularise the problem and improve its convergence properties. Several benchmarks are presented to show the accuracy and robustness of the proposed method and its great potential to enable the robust and effective identification of patient-specific, heterogeneous physical properties, s.a. tissue stiffness properties. In particular, we demonstrate the capability of the PINN to detect the presence, location and severity of scar tissue, which is beneficial to develop personalised simulation models for disease diagnosis, especially for cardiac applications.

The Verwey transition in magnetite is a benchmark electronically driven phase transition that is highly sensitive to lattice imperfections and external perturbations. Doping, deviations from oxygen stoichiometry, and irradiation-induced point defects are known to lower the Verwey transition temperature, T_{rm V}. By contrast, the role of remanent strain fields and extended defect structures generated by uniaxial stress has remained largely unexplored. Here we combine dark-field x-ray microscopy (DFXM) and ac magnetic susceptibility to determine how strain-induced defects affect the Verwey transition in stoichiometric single-crystalline magnetite after uniaxial compression and unloading. The DFXM measurements were performed on two samples compressed along the same [011] direction: loading to 200~MPa generated stable line-like defects and remanent strain fields, whereas loading beyond the fracture threshold produced denser defect networks and mechanical fracture. To test the effect of a different loading geometry, we also measured the ac susceptibility of a sample fractured by compression along [001]. Real-space DFXM imaging, lattice-orientation mapping, and residual strain mapping show substantial remanent structural disorder after compression. Nevertheless, neither the transition temperature T_{rm V} nor the sharpness of the transition changes measurably in any of the compressed or fractured samples. This behavior contrasts with the strong suppression of T_{rm V} by point-like disorder. Our results show that extended line-like defects and remanent strain fields produced by plastic deformation do not measurably perturb the macroscopic electronic ordering responsible for the Verwey transition, thereby distinguishing the effects of point defects from those of extended slip-related defects in magnetite.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

This research paper explores the impact of various input parameters, including Infill percentage, Layer Height, Extrusion Temperature, and Print Speed, on the resulting Tensile Strength in objects produced through additive manufacturing. The main objective of this study is to enhance our understanding of the correlation between the input parameters and Tensile Strength, as well as to identify the key factors influencing the performance of the additive manufacturing process. To achieve this objective, we introduced the utilization of Explainable Artificial Intelligence (XAI) techniques for the first time, which allowed us to analyze the data and gain valuable insights into the system's behavior. Specifically, we employed SHAP (SHapley Additive exPlanations), a widely adopted framework for interpreting machine learning model predictions, to provide explanations for the behavior of a machine learning model trained on the data. Our findings reveal that the Infill percentage and Extrusion Temperature have the most significant influence on Tensile Strength, while the impact of Layer Height and Print Speed is relatively minor. Furthermore, we discovered that the relationship between the input parameters and Tensile Strength is highly intricate and nonlinear, making it difficult to accurately describe using simple linear models.

This work puts forth a new optimal design formulation for planar elastic membranes. The goal is to minimize the membrane's compliance through choosing the material distribution described by a positive Radon measure. The deformation of the membrane itself is governed by the convexified F\"{o}ppl's model. The uniqueness of this model lies in the convexity of its variational formulation despite the inherent nonlinearity of the strain-displacement relation. It makes it possible to rewrite the optimization problem as a pair of mutually dual convex variational problems. In the primal problem a linear functional is maximized with respect to displacement functions while enforcing that point-wisely the strain lies in an unbounded closed convex set. The dual problem consists in finding equilibrated stresses that are to minimize a convex integral functional of linear growth defined on the space of Radon measures. The pair of problems is analysed: existence and regularity results are provided, together with the system of optimality criteria. To demonstrate the computational potential of the pair, a finite element scheme is developed around it. Upon reformulation to a conic-quadratic & semi-definite programming problem, the method is employed to produce numerical simulations for several load case scenarios.

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, and the shape of the particle is exactly resolved as one of the coordinate surfaces representing the inner boundary of the computational domain. As the prolate spheroidal grid is naturally clustered near the particle surface, good resolution is obtained in the regions where the gradients of relevant flow variables are most significant. This coordinate system also allows large domain sizes with a reasonable number of mesh points to simulate unbounded fluid around a particle. Changing the aspect ratio of the inner computational boundary enables simulations of different particle shapes ranging from a sphere to a slender fiber. Numerical studies of the latter particle shape allow testing of slender body theories. The mass and momentum equations are solved with a Schur complement approach allowing us to solve the zero inertia case necessary to isolate the viscoelastic effects. The singularities associated with the coordinate system are overcome using L'Hopital's rule. A straightforward imposition of conditions representing a time-varying combination of linear flows on the outer boundary allows us to study various flows with the same computational domain geometry. {For the special but important case of zero fluid and particle inertia we obtain a novel formulation that satisfies the force- and torque-free constraint in an iteration-free manner.} The numerical method is demonstrated for various flows of Newtonian and viscoelastic fluids around spheres and spheroids (including those with large aspect ratio). Good agreement is demonstrated with existing theoretical and numerical results.

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

In this work, we investigate the transient rheological behavior of two soft glassy materials: a clay dispersion and a silica gel, emphasizing their unconventional shear stress build-up behavior under conditions of constant imposed strain. For both materials, the elastic modulus and static yield stress undergo time-dependent evolution or aging. In addition, following an intense period of pre-shearing (i.e. shear-melting or destructuration), the material relaxation time is observed to show a stronger than linear dependence on the sample age, suggestive of hyper-aging dynamics. We show that these features are consistent with non-monotonic steady-state shear stress/shear rate flow curves characterized by a local stress minimum. When a steady shear flow is suddenly ceased, and the total imposed sample strain is held constant, both materials show an initial relaxation of the shear stress followed by a period of shear stress buildup, resulting in a local minimum in the evolution of shear stress with time. For the clay dispersion, the intensity of these effects increases with higher pre-shear rates, whereas for the silica gel, the effects are largely independent of the pre-shear rate. We also propose a simple time-dependent linear Maxwell model, which qualitatively predicts the experimentally observed trends in which the shear stress build-up is directly related to a monotonic increase in the elastic modulus, giving keen insight into this peculiar phenomenon.

The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. This morphing is obtained by deforming a reference shape, through the resolution of a sequence of linear elasticity equations, onto the target shape. In particular, our approach does not assume any knowledge of a boundary parametrization. Furthermore, we demonstrate how constraints can be imposed on specific points, lines and surfaces in the reference domain to ensure alignment with their counterparts in the target domain after morphing. Additionally, we show how the proposed methodology can be integrated in an offline and online paradigm, which is useful in reduced-order modeling scenarii involving variable shapes. This framework facilitates the efficient computation of the morphings in various geometric configurations, thus improving the versatility and applicability of the approach. The methodology is illustrated on the regression problem of the drag and lift coefficients of airfoils of non-parameterized variable shapes.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements. The effectiveness of this approach is demonstrated through material design experiments requiring adherence to precise morphometric properties, challenging inverse design tasks involving the generation of materials inducing specific stress-strain responses, and copyright-constrained content generation tasks. All code has been released at https://github.com/RAISELab-atUVA/Constrained-Stable-Diffusion.

Sycophancy in LLMs is documented across 70+ papers, but expert agreement on construct boundaries remains low (ICC=.184; Ye et al., 2026). The construct fragments because behavioral classification depends on which surface form is privileged. We adopt a materials-science framing: conversation as test specimen under load, LLM-model as material charge, pushback as progressive load, stance-flip as material failure. We characterize this failure across three loading cases (debate n=1000; false-presuppositions n=3400; ethical-setting n=3400; 10-17 material charges per case; 7800 specimens total) using 14 turn-level axis-measurements spanning velocity, damage accumulation, frame-drift, brittleness, and direction stability, plus three speaker-resolved axes from an independent pipeline. The measurements are Hooke-coupled (σ= E cdot varepsilon analog) and reproduce across loading cases with effects up to |r_{rb}| = 0.35 on debate; the sign structure adds a second pattern: the ethical-setting case inverts the velocity and accumulation blocks. Variance composition partitions into two profiles: debate is charge-dominated (brittle-fracture-like: the material grade decides), false-presuppositions and ethical-setting are topic-dominated (creep-like: the load decides); the ratios (2.03 vs 0.13/0.17) are estimator-dependent, for debate even in direction. Cross-judge reliability (GPT-4o vs Haiku 4.5) shows debate scoring is judge-robust (Cohen's κ= 0.88) while false-presupposition scoring is judge-sensitive (κ= 0.36) -- a caveat single-judge benchmarks must report. This is the methodological move Ye et al.'s diagnosis calls for: a multi-axis characterization that does not depend on which surface form of the construct one privileges.

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology, geophysics, astrophysics and fluid dynamics. In the PINN framework, the governing partial differential equations, along with initial and boundary conditions, are encoded directly into the loss function, enabling the network to learn solutions that are consistent with the underlying physics. In this work, we employ the PINN framework to solve the dimensionless Navier-Stokes equations for three two-dimensional incompressible, steady, laminar flow problems without using any labeled data. The boundary and initial conditions are enforced in a hard manner, ensuring they are satisfied exactly rather than penalized during training. We validate the PINN predicted velocity profiles, drag coefficients and pressure profiles against the conventional computational fluid dynamics (CFD) simulations for moderate to high values of Reynolds number (Re). It is observed that the PINN predictions show good agreement with the CFD results at lower Re. We also extend our analysis to a transient condition and find that our method is equally capable of simulating complex time-dependent flow dynamics. To quantitatively assess the accuracy, we compute the L_2 normalized error, which lies in the range O(10^{-4}) - O(10^{-1}) for our chosen case studies.

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.

Bridge scour is a complex phenomenon combining hydrological, geotechnical and structural processes. Bridge scour is the leading cause of bridge collapse, which can bring catastrophic consequences including the loss of life. Estimating scour on bridges is an important task for engineers assessing bridge system performance. Overestimation of scour depths during design may lead to excess spendings on construction whereas underestimation can lead to the collapse of a bridge. Many empirical equations have been developed over the years to assess scour depth at bridge piers. These equations have only been calibrated with laboratory data or very few field data. This paper compares eight equations including the UK CIRIA C742 approach to establish their accuracy using the open access USGS pier-scour database for both field and laboratory conditions. A one-at-the-time sensitivity assessment and a global sensitivity analysis were then applied to identify the most significant parameters in the eight scour equations. The paper shows that using a global approach, i.e. one where all parameters are varied simultaneously, provides more insights than a traditional one-at-the-time approach. The main findings are that the CIRIA and Froehlich equations are the most accurate equations for field conditions, and that angle of attack, pier shape and the approach flow depth are the most influential parameters. Efforts to reduce uncertainty of these three parameters would maximise increase of scour estimate precision.

Spider silks are remarkable materials characterized by superb mechanical properties such as strength, extensibility and lightweightedness. Yet, to date, limited models are available to fully explore sequence-property relationships for analysis and design. Here we propose a custom generative large-language model to enable design of novel spider silk protein sequences to meet complex combinations of target mechanical properties. The model, pretrained on a large set of protein sequences, is fine-tuned on ~1,000 major ampullate spidroin (MaSp) sequences for which associated fiber-level mechanical properties exist, to yield an end-to-end forward and inverse generative strategy. Performance is assessed through: (1), a novelty analysis and protein type classification for generated spidroin sequences through BLAST searches, (2) property evaluation and comparison with similar sequences, (3) comparison of molecular structures, as well as, and (4) a detailed sequence motif analyses. We generate silk sequences with property combinations that do not exist in nature, and develop a deep understanding the mechanistic roles of sequence patterns in achieving overarching key mechanical properties (elastic modulus, strength, toughness, failure strain). The model provides an efficient approach to expand the silkome dataset, facilitating further sequence-structure analyses of silks, and establishes a foundation for synthetic silk design and optimization.

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

Through evolution, nature has presented a set of remarkable protein materials, including elastins, silks, keratins and collagens with superior mechanical performances that play crucial roles in mechanobiology. However, going beyond natural designs to discover proteins that meet specified mechanical properties remains challenging. Here we report a generative model that predicts protein designs to meet complex nonlinear mechanical property-design objectives. Our model leverages deep knowledge on protein sequences from a pre-trained protein language model and maps mechanical unfolding responses to create novel proteins. Via full-atom molecular simulations for direct validation, we demonstrate that the designed proteins are novel, and fulfill the targeted mechanical properties, including unfolding energy and mechanical strength, as well as the detailed unfolding force-separation curves. Our model offers rapid pathways to explore the enormous mechanobiological protein sequence space unconstrained by biological synthesis, using mechanical features as target to enable the discovery of protein materials with superior mechanical properties.

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

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

Origami metamaterials typically consist of folded sheets with periodic patterns, conferring them with remarkable mechanical properties. In the context of Continuum Mechanics, the majority of existing predictive methods are mechanism analogs which favor rigid folding and panel bending. While effective in predicting primary deformation modes, existing methods fall short in capturing the full spectrum of deformation of non-rigid foldable origami, such as the emergence of curvature along straight creases, local strain at vertices and warpage in panels. To fully capture the entire deformation spectrum and enhance the accuracy of existing methods, this paper introduces a homogenization framework for origami metamaterials where the faces are modeled as plate elements. Both asymptotic and energy-based homogenization methods are formulated and implemented. As a representative crease pattern, we examine the Miura origami sheet homogenized as an equivalent Kirchhoff-Love plate. The results reveal that certain effective elastic properties are nonlinearly related to both the initial fold angle and the crease stiffness. When benchmarked with results from fully resolved simulations, our framework yields errors up to 12.9\%, while existing models, including the bar-and-hinge model and the rigid-panel model, show up to 161\% error. The differences in errors are associated with the complex modes of crease and panel deformation in non-rigid origami, unexplored by the existing models. This work demonstrates a precise and efficient continuum framework for origami metamaterials as an effective strategy for predicting their elastic properties, understanding their mechanics, and designing their functionalities.

Focusing on simulated dilute polymer solutions, this letter investigates the interactions between flow structures and organized polymer stress sheets for the steady arrowhead coherent structure in a two-dimensional periodic channel flow. Formulating the problem in a frame of reference moving with the arrowhead velocity, streamlines, which are also pathlines in this frame, enables the identification of two distinct topological regions linked to two stagnation points. The streamlines help connecting the spatial distribution of polymer stress within the sheets and the dynamics of polymers transported by the flow. Using stresslines, lines parallel to the eigenvectors of polymer stress, a novel formulation of the viscoelastic stress term in the momentum transport equation proposes a more intuitive interpretation of the relation between the curvature of the stresslines, and the variation of stress along these lines, with the local flow topology. An approximation of this formulation is shown to explain the pressure jump observed in the arrowhead structure as a function of the local curvature of the polymer stress sheet.

Critical temperature, T_c, and the transition width, ΔT_c, are two primary parameters of the superconducting transition. The latter parameter reflects the superconducting state disturbance originating from the thermodynamic fluctuations, atomic disorder, applied magnetic field, the presence of secondary crystalline phases, applied pressure, etc. Recently, Hirsch and Marsiglio (2020 arXiv:2012.12796) performed an analysis of the transition width in several near-room-temperature superconductors (NRTS) and reported that the reduced transition width, ΔT_c/T_c, in these materials does not follow a conventional trend of transition width broadening on applied magnetic field observed in low- and high-T_c superconductors. Here we present thorough mathematical analysis of the magnetoresistive data, R(T,B), for the high-entropy alloy (ScZrNb)_{0.65}[RhPd]_{0.35} and hydrogen-rich superconductors of Im-3m-H_{3}S, C2/m-LaH_{10} and P63/mmc-CeH_9. We found that the reduced transition width, ΔT_c/T_c, in these materials does follow a conventional broadening trend on applied magnetic field.

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

Data-driven approaches have revolutionized 3D vision, enabling transformers to effectively reconstruct and generate static 3D objects. However, generating simulative 4D dynamics -- realistic temporal deformations of static objects under various physical conditions -- remains challenging and often ad hoc, despite its importance in building comprehensive 3D world models. Most existing methods assume a predefined physical model and use system identification to estimate parameters, restricting these methods to specific categories and small-scale datasets. We propose that these restrictions can be overcome by learning a data-driven kinematic state parameterization for object-centric physical systems. Specifically, we learn both a latent space representing all possible states of the object and a decoder that maps any sampled latent to a plausibly deformed shape of the object. We refer to this parameterization as Neural Object Kinematics (NeuROK), and learn a transformer-based encoder-decoder model on a curated large-scale 4D dataset. This formulation and the learned model significantly simplify the generation of simulative dynamics since we only need to consider the dynamics within a low-dimensional latent space from the Lagrangian mechanics' perspective in classical physics. We demonstrate the effectiveness and generality of this neural simulation framework across diverse dynamic object types, showing clear advantages over prior works. Project page: https://chen-geng.com/neurok

Neural surrogates and operator networks for solving partial differential equation (PDE) problems have attracted significant research interest in recent years. However, most existing approaches are limited in their ability to generalize solutions across varying non-parametric geometric domains. In this work, we address this challenge in the context of Polyethylene Terephthalate (PET) bottle buckling analysis, a representative packaging design problem conventionally solved using computationally expensive finite element analysis (FEA). We introduce a hybrid DeepONet-Transolver framework that simultaneously predicts nodal displacement fields and the time evolution of reaction forces during top load compression. Our methodology is evaluated on two families of bottle geometries parameterized by two and four design variables. Training data is generated using nonlinear FEA simulations in Abaqus for 254 unique designs per family. The proposed framework achieves mean relative L^{2} errors of 2.5-13% for displacement fields and approximately 2.4% for time-dependent reaction forces for the four-parameter bottle family. Point-wise error analyses further show absolute displacement errors on the order of 10^{-4}-10^{-3}, with the largest discrepancies confined to localized geometric regions. Importantly, the model accurately captures key physical phenomena, such as buckling behavior, across diverse bottle geometries. These results highlight the potential of our framework as a scalable and computationally efficient surrogate, particularly for multi-task predictions in computational mechanics and applications requiring rapid design evaluation.

Hyperelastic models have been widely used to model polymers and soft tissues. However, most hyperelastic models are phenomenological material models. Based on statistical mechanics and molecular chain configuration, 8 chain model or Arruda-Boyce model is a physical model which can be used to understand how microstructures of chains affect macroscopic mechanical properties of polymers and soft tissues. Mechanical properties of many polymers and soft tissues are directional dependent. Polymer matrix can be reinforced by fibers. For soft tissues, ligaments and tendons will lead to anisotropic properties. Since matrix and reinforcements are composed of similar microstructural molecular chains, they can be modeled by using the same mathematical model. In this paper, a series of 8 chain models is used to understand composite properties. That is, an isotropic 8 chain model will be used to model matrix and anisotropic 8 chain models will be used to model fibers. Replacing I_1 in isotropic 8 chain model with I_4 in anisotropic 8 chain model is physically corresponding to changing representative 8 chain cubic cell to 8 chain slender cell. This treatment not only simplifies exist anisotropic mathematical structures but also keeps microscopic physics of 8 chain model unchanged.

Modeling deformable objects - especially continuum materials - in a way that is physically plausible, generalizable, and data-efficient remains challenging across 3D vision, graphics, and robotic manipulation. Many existing methods oversimplify the rich dynamics of deformable objects or require large training sets, which often limits generalization. We introduce embodied MPM (EMPM), a deformable object modeling and simulation framework built on a differentiable Material Point Method (MPM) simulator that captures the dynamics of challenging materials. From multi-view RGB-D videos, our approach reconstructs geometry and appearance, then uses an MPM physics engine to simulate object behavior by minimizing the mismatch between predicted and observed visual data. We further optimize MPM parameters online using sensory feedback, enabling adaptive, robust, and physics-aware object representations that open new possibilities for robotic manipulation of complex deformables. Experiments show that EMPM outperforms spring-mass baseline models. Project website: https://embodied-mpm.github.io.

We show that Hertzian particle contacts are the underlying cause of the as-yet-unexplained noninteger power laws in weakly nonlinear rheology. In the medium amplitude oscillatory shear (MAOS) region, the cubic scaling of the leading order nonlinear shear stress (σ_3 sim γ_0^{m_3}, m_3=3) is the standard expectation. Expanding on the work by Natalia et al. [J. Rheol. 64 625-635 (2020)], we report an extensive data set of noncubical, noninteger power law scalings m_3 for particle suspensions in two immiscible fluids with a capillary attractive interaction, known as capillary suspensions. Here, we show that distinct power law exponents are found for the storage and loss moduli and these noninteger scalings occur at every secondary fluid concentration for two different contact angles. These compelling results indicate that the noninteger scalings are related to the underlying microstructure of capillary suspensions. We show that the magnitude of the third harmonic elastic stress scaling m_3,elastic originates from Hertzian-like contacts in combination with the attractive capillary force. The related third harmonic viscous stress scaling m_3,viscous is, found to be associated with adhesive-controlled friction. These observations, conducted for a wide range of compositions, can help explain previous reports of noninteger scaling for materials involving particle contacts and offers a new opportunity using the variable power law exponent of MAOS rheology to reveal the physics of particle bonds and friction in the rheological response under low deformation instead of at very high shear rates.

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

In this work, we present a method to generate a configurational level fingerprint for polymers using the Bead-Spring-Model. Unlike some of the previous fingerprinting approaches that employ monomer-level information where atomistic descriptors are computed using quantum chemistry calculations, this approach incorporates configurational information from a coarse-grained model of a long polymer chain. The proposed approach may be advantageous for the study of behavior resulting from large molecular weights. To create this fingerprint, we make use of two kinds of descriptors. First, we calculate certain geometric descriptors like Re2, Rg2 etc. and label them as Calculated Descriptors. Second, we generate a set of data-driven descriptors using an unsupervised autoencoder model and call them Learnt Descriptors. Using a combination of both of them, we are able to learn mappings from the structure to various properties of the polymer chain by training ML models. We test our fingerprint to predict the probability of occurrence of a configuration at equilibrium, which is approximated by a simple linear relationship between the instantaneous internal energy and equilibrium average internal energy.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

The precision, stability, and performance of lightweight high-strength steel structures in heavy machinery is affected by their highly nonlinear dynamics. This, in turn, makes control more difficult, simulation more computationally intensive, and achieving real-time autonomy, using standard approaches, impossible. Machine learning through data-driven, physics-informed and physics-inspired networks, however, promises more computationally efficient and accurate solutions to nonlinear dynamic problems. This study proposes a novel framework that has been developed to estimate real-time structural deflection in hydraulically actuated three-dimensional systems. It is based on SLIDE, a machine-learning-based method to estimate dynamic responses of mechanical systems subjected to forced excitations.~Further, an algorithm is introduced for the data acquisition from a hydraulically actuated system using randomized initial configurations and hydraulic pressures.~The new framework was tested on a hydraulically actuated flexible boom with various sensor combinations and lifting various payloads. The neural network was successfully trained in less time using standard parameters from PyTorch, ADAM optimizer, the various sensor inputs, and minimal output data. The SLIDE-trained neural network accelerated deflection estimation solutions by a factor of 10^7 in reference to flexible multibody simulation batches and provided reasonable accuracy. These results support the studies goal of providing robust, real-time solutions for control, robotic manipulators, structural health monitoring, and automation problems.

We consider the dictionary-based ROM-net (Reduced Order Model) framework [T. Daniel, F. Casenave, N. Akkari, D. Ryckelynck, Model order reduction assisted by deep neural networks (ROM-net), Advanced modeling and Simulation in Engineering Sciences 7 (16), 2020] and summarize the underlying methodologies and their recent improvements. The main contribution of this work is the application of the complete workflow to a real-life industrial model of an elastoviscoplastic high-pressure turbine blade subjected to thermal, centrifugal and pressure loadings, for the quantification of the uncertainty on dual quantities (such as the accumulated plastic strain and the stress tensor), generated by the uncertainty on the temperature loading field. The dictionary-based ROM-net computes predictions of dual quantities of interest for 1008 Monte Carlo draws of the temperature loading field in 2 hours and 48 minutes, which corresponds to a speedup greater than 600 with respect to a reference parallel solver using domain decomposition, with a relative error in the order of 2%. Another contribution of this work consists in the derivation of a meta-model to reconstruct the dual quantities of interest over the complete mesh from their values on the reduced integration points.

We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress values. This method is based in representing a periodic micro-structure as a graph, combined with a message passing graph neural network. We are able to retrieve local stress field distributions, providing average stress values produced by a mean field reduced order model (ROM) or Finite Element (FE) simulation at the macro-scale. The prediction of local stress fields are of utmost importance considering fracture analysis or the definition of local fatigue criteria. Our model incorporates physical constraints during training to constraint local stress field equilibrium state and employs a periodic graph representation to enforce periodic boundary conditions. The benefits of the proposed physics-informed GNN are evaluated considering linear and non linear hyperelastic responses applied to varying geometries. In the non-linear hyperelastic case, the proposed method achieves significant computational speed-ups compared to FE simulation, making it particularly attractive for large-scale applications.

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing PINNs are based on point-wise formulation with fully-connected networks to learn continuous functions, which suffer from poor scalability and hard boundary enforcement. Second, the infinite search space over-complicates the non-convex optimization for network training. Third, although the convolutional neural network (CNN)-based discrete learning can significantly improve training efficiency, CNNs struggle to handle irregular geometries with unstructured meshes. To properly address these challenges, we present a novel discrete PINN framework based on graph convolutional network (GCN) and variational structure of PDE to solve forward and inverse partial differential equations (PDEs) in a unified manner. The use of a piecewise polynomial basis can reduce the dimension of search space and facilitate training and convergence. Without the need of tuning penalty parameters in classic PINNs, the proposed method can strictly impose boundary conditions and assimilate sparse data in both forward and inverse settings. The flexibility of GCNs is leveraged for irregular geometries with unstructured meshes. The effectiveness and merit of the proposed method are demonstrated over a variety of forward and inverse computational mechanics problems governed by both linear and nonlinear PDEs.

Scientific discovery is not only answer generation but revision of the representational regime in which evidence, artifacts, operations, and verifiers are typed. We develop a category-theoretic account of agentic discovery for materials science. In a fixed regime b with schema category S_b, the system state is a copresheaf I_t: S_b -> Set, and provenance is the category of elements \int_{S_b} I_t. Fixed-regime operation is an update on such states, endofunctorial only when provenance-preserving refinements are specified and preserved. Discovery is instead a verified regime transition u: S_b -> S_b': old artifacts are preserved, transported by the left Kan extension Lan_u I_t, and compared with the post-transition state to identify residual content beyond functorial transport. This separates retrieval, search, and discovery without subjective novelty. We instantiate the framework in two systems. In Builder/Breaker, a protein-mechanics world model is revised under a Minimum Description Length gate; the accepted law expresses within-chain flexibility as all-mode elastic compliance conditioned by slow collective-mode participation, or mode-conditioned compliance. In CategoryScienceClaw, typed skills, artifacts, open needs, workflow mutation, gates, stress tests, and public discourse become a proof-carrying knowledge-computation graph. A fiber-network example records candidate models, rejected alternatives, an AIC gate, perturbation tests, and an accepted orientation-tensor anisotropic stiffness surrogate over an isotropic fiber-count descriptor. Together, the cases show how category theory can be both a mathematical language for discovery and an engineering specification for self-revising AI discovery systems.

Efficient and accurate prediction of material properties is critical for advancing materials design and applications. The rapid-evolution of large language models (LLMs) presents a new opportunity for material property predictions, complementing experimental measurements and multi-scale computational methods. We focus on predicting the elastic constant tensor, as a case study, and develop domain-specific LLMs for predicting elastic constants and for materials discovery. The proposed ElaTBot LLM enables simultaneous prediction of elastic constant tensors, bulk modulus at finite temperatures, and the generation of new materials with targeted properties. Moreover, the capabilities of ElaTBot are further enhanced by integrating with general LLMs (GPT-4o) and Retrieval-Augmented Generation (RAG) for prediction. A specialized variant, ElaTBot-DFT, designed for 0 K elastic constant tensor prediction, reduces the prediction errors by 33.1% compared with domain-specific, material science LLMs (Darwin) trained on the same dataset. This natural language-based approach lowers the barriers to computational materials science and highlights the broader potential of LLMs for material property predictions and inverse design.

Accurate mechanical properties (or materials) Young's modulus (E), Poisson's ratio (ν) and density (ρ) are essential for reliable physics simulation of digital worlds, but most 3D assets lack this information. We propose AdaVoMP, a method for predicting accurate dense spatially-varying (E, ν, ρ) for input 3D objects across representations, improving the resolution, accuracy, and memory efficiency over the state-of-the-art. The foundation of our technique is a sparse and adaptive voxel structure SAV that efficiently represents both the input 3D shape and the material field output. We replace the fixed-voxel model of the most accurate prior method, VoMP, with a novel sparse transformer encoder-decoder model that learns to generate a unique SAV autoregressively for every input shape to represent its materials, achieving a resolution 16^3times higher than prior art. Experiments show that AdaVoMP estimates more accurate volumetric properties, even with lesser test-time compute than all prior art. This allows us to convert high-resolution complex 3D objects into simulation-ready assets, resulting in realistic deformable simulations.

In the applications of proxy-SU(3) model in the context of determining (beta,gamma) values for nuclei across the periodic table, for understanding the preponderance of triaxial shapes in nuclei with Z ge 30, it is seen that one needs not only the highest weight (hw) or leading SU(3) irreducible representation (irrep) (lambda_H, mu_H) but also the lower SU(3) irreps (lambda ,mu) such that 2lambda + mu =2lambda_H + mu_H-3r with r=0,1 and 2 [Bonatsos et al., Symmetry {\bf 16}, 1625 (2024)]. These give the next highest weight (nhw) irrep, next-to-next highest irrep (nnhw) and so on. Recently, it is shown that for nuclei with 32 le Z,N le 46, there will be not only proxy-SU(3) but also proxy-SU(4) symmetry [Kota and Sahu, Physica Scripta {\bf 99}, 065306 (2024)]. Following these developments, presented in this paper are the SU(3) irreps (lambda ,mu) with 2lambda + mu =2lambda_H + mu_H-3r, r=0,1,2 for various isotopes of Ge, Se, Kr, Sr, Zr, Mo, Ru and Pd (with 32 le N le 46) assuming good proxy-SU(4) symmetry. A simple method for obtaining the SU(3) irreps is described and applied. The tabulations for proxy-SU(3) irreps provided in this paper will be useful in further investigations of triaxial shapes in these nuclei.

In recent years, there has been rapid development in 3D generation models, opening up new possibilities for applications such as simulating the dynamic movements of 3D objects and customizing their behaviors. However, current 3D generative models tend to focus only on surface features such as color and shape, neglecting the inherent physical properties that govern the behavior of objects in the real world. To accurately simulate physics-aligned dynamics, it is essential to predict the physical properties of materials and incorporate them into the behavior prediction process. Nonetheless, predicting the diverse materials of real-world objects is still challenging due to the complex nature of their physical attributes. In this paper, we propose Physics3D, a novel method for learning various physical properties of 3D objects through a video diffusion model. Our approach involves designing a highly generalizable physical simulation system based on a viscoelastic material model, which enables us to simulate a wide range of materials with high-fidelity capabilities. Moreover, we distill the physical priors from a video diffusion model that contains more understanding of realistic object materials. Extensive experiments demonstrate the effectiveness of our method with both elastic and plastic materials. Physics3D shows great potential for bridging the gap between the physical world and virtual neural space, providing a better integration and application of realistic physical principles in virtual environments. Project page: https://liuff19.github.io/Physics3D.

This paper puts forward an integrated microstructure design methodology that replaces the common existing design approaches: 1) reconstruction of microstructures, 2) analyzing and quantifying material properties, and 3) inverse design of materials using deep-learned generative and surrogate models. The long-standing issue of microstructure reconstruction is well addressed in this study using a new class of state-of-the-art generative model, the diffusion-based generative model (DGM). Moreover, the conditional formulation of DGM for guidance to the embedded desired material properties with a transformer-based attention mechanism enables the inverse design of multifunctional composites. A convolutional neural network (CNN)-based surrogate model is utilized to analyze the nonlinear material behavior to facilitate the prediction of material properties for building microstructure-property linkages. Combined, these generative and surrogate models enable large data processing and database construction that is often not affordable with resource-intensive finite element method (FEM)-based direct numerical simulation (DNS) and iterative reconstruction methods. An example case is presented to demonstrate the effectiveness of the proposed approach, which is designing mechanoluminescence (ML) particulate composites made of europium and dysprosium ions. The results show that the inversely-designed multiple ML microstructure candidates with the proposed generative and surrogate models meet the multiple design requirements (e.g., volume fraction, elastic constant, and light sensitivity). The evaluation of the generated samples' quality and the surrogate models' performance using appropriate metrics are also included. This assessment demonstrates that the proposed integrated methodology offers an end-to-end solution for practical material design applications.

Body deformation caused by muscle contraction plays a vital role in the visual realism of character animation, yet in most 3D animation pipelines artists have to manually specify muscle activations, which is time-consuming and gives no guarantee of physical realism. To address this, we propose a new method in which a reinforcement learning (RL) controller discovers per-muscle activations that track reference motions without manual tuning. Existing RL muscle controllers stop at 1D muscles; we go one step further, keeping the 1D model inside the RL control loop as a fast surrogate, and using a 3D volumetric simulation to produce the final deformation. Because both stages share the very same constitutive law, the muscle deformation is produced by the same activations that generated the motion. We further add a measured electromyography (EMG) prior that steers the redundant activation solution toward real human muscle recruitment. To achieve stable, efficient, and realistic simulation, we propose a novel geometric multigrid for Extended Position-Based Dynamics (XPBD) that is built on a coarse tetrahedral cage with barycentric-coordinate prolongation and closes a V-cycle on tetrahedral meshes. Within this GPU-parallelized solver, we inject the same Hill-type force-length law as an energy-based fiber constraint that turns per-fiber activation into realistic muscle contraction and bulging. We demonstrate volumetric muscle simulation on a 194-muscle human body with a diverse set of motions (walk, kick, swim, overhead-squat, etc.), simulating the full-body model at 18 ms per frame on a single RTX 4090. Our work takes a step toward character animation that is not only visually convincing but also biomechanically grounded. The website with code and videos is at https://chunleili.github.io/project-page-rlmuscle/.

As LLMs advance their reasoning capabilities about the physical world, the absence of rigorous benchmarks for evaluating their ability to generate scientifically valid physical models has become a critical gap. Computational mechanics, which develops and applies mathematical models and numerical methods to predict the behavior of physical systems under forces, deformation, and constraints, provides an ideal foundation for structured scientific reasoning evaluation. Problems follow clear mathematical structure, enforce strict physical and numerical constraints, and support objective verification. The discipline requires constructing explicit models of physical systems and reasoning about geometry, spatial relationships, and material behavior, connecting directly to emerging AI goals in physical reasoning and world modeling. We introduce FEM-Bench, a computational mechanics benchmark designed to evaluate the ability of LLMs to generate correct finite element method (FEM) and related code. FEM-Bench 2025 contains a suite of introductory but nontrivial tasks aligned with material from a first graduate course on computational mechanics. These tasks capture essential numerical and physical modeling challenges while representing only a small fraction of the complexity present in the discipline. Despite their simplicity, state-of-the-art LLMs do not reliably solve all of them. In a five attempt run, the best performing model at function writing, Gemini 3 Pro, completed 30/33 tasks at least once and 26/33 tasks all five times. The best performing model at unit test writing, GPT-5, had an Average Joint Success Rate of 73.8%. Other popular models showed broad performance variation. FEM-Bench establishes a structured foundation for evaluating AI-generated scientific code, and future iterations will incorporate increasingly sophisticated tasks to track progress as models evolve.

The NMR measurements performed on a single orthorhombic crystal of superconducting ferromagnet UCoGe (Y.Ihara et al, Phys. Rev. Lett. v.105, 206403 (2010)) demonstrate strongly anisotropic magnetic properties of this material. The presented calculations allow to establish the dependence of longitudinal spin-lattice relaxation rate from temperature and magnetic field. The value 1/T_1T in field perpendicular to spontaneous magnetisation directed along c-axis has maximum in vicinity of Curie temperature whereas it does not reveal similar behaviour in field parallel to the direction of spontaneous magnetisation. Also there was shown that the longitudinal spin-lattice relaxation rate is strongly field dependent when the field directed in b-crystallographic direction but field independent if magnetic field is oriented along a-axis.

Improvised explosives used for fishing on shallow Indonesian reefs shatter coral skeleton, yet the damage they cause has been described largely through empirical radii and ecological surveys. We formulate an idealized model of how free gas held within a coral canopy modifies the shock loading that such a charge delivers to skeletal plates. The canopy is treated as a relaxed bubbly mixture whose shock impedance follows from the conservation of mass and momentum, and the reef is represented as a layered column of water, canopy, skeletal plate, and canopy struck at normal incidence. Three closed-form results emerge. Above a crossover pressure set by the void fraction and the stiffness of seawater, the canopy becomes nearly transparent to the shock. The impulse transmitted through any lossless layered stack is independent of the canopy, so gas redistributes the pulse in time without changing its total push. A plate carries tension after reflection from its lower face only when the canopy impedance falls below a threshold fixed by the plate thickness and the pulse duration, which defines a critical thickness. For a one-kilogram charge directly overhead, a gas-rich canopy more than triples the standoff at which a twelve-centimeter plate spalls while shortening the standoff at which it is crushed. A prescribed daily cycle of photosynthetic gas makes the same charge markedly more damaging at noon than at night. Bubble dynamics show that the canopy does not reach equilibrium within the pulse, so the results are best read as upper bounds.

We study the parameter dependence and transversality properties of trajectories of the controlled ODE $ U_x = P, qquad P_x = - f(U) - βP + tilde α(x)U, arising from traveling-wave solutions of a bistable reaction-diffusion equation with control. Optimal profiles minimizing the L^1-norm of the control \tilde α are determined by the unstable and stable manifolds Γ_u, Γ_s, the critical curve P^*(U) = Uf(U), and the associated function F(U) = dP^*{dU} + f(U){P^*(U)}. We establish generic transversality properties for these objects with respect to perturbations of the speed β and the nonlinear source f, together with quantitative estimates on the first- and second-order dependence of the invariant manifolds on these parameters. We also analyze the loss of regularity at the critical speed β^{**}, where the unstable manifold approaches the strongly stable manifold of the equilibrium (U^*,0)$. These results provide the ODE ingredients used in the analysis of the structure and regularity of optimal profiles in paper [S. Bianchini and C. Trifone. Traveling profiles and control cost for a PDE describing the evolution of invasive species. 2026. arXiv: 2606.23979 [math.OC]].

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural operator (FNO) show promise in accelerating the solution of parametric partial differential equations (PDEs), the lack of explicit physical constraints, may limit generalisation and long-term accuracy for complex phase-field dynamics. Here, we develop a physics-informed neural operator framework to learn parametric phase-field PDEs, namely PF-PINO. By embedding the residuals of phase-field governing equations into the data-fidelity loss function, our framework effectively enforces physical constraints during training. We validate PF-PINO against benchmark phase-field problems, including electrochemical corrosion, dendritic crystal solidification, and spinodal decomposition. Our results demonstrate that PF-PINO significantly outperforms conventional FNO in accuracy, generalisation capability, and long-term stability. This work provides a robust and efficient computational tool for phase-field modelling and highlights the potential of physics-informed neural operators to advance scientific machine learning for complex interfacial evolution problems.

Large language models can answer scientific questions, yet a correct output does not reveal whether the model represents or uses the governing physics. Here we show that materials science mechanism information in the open-weight google/gemma-4-E4B-it model has three experimentally separable forms: concepts are readable in individual hidden states, constitutive orientation is carried by controlled transformations between states, and selected internal representations causally control engineering answers. We combine matched direct and Jacobian vocabulary readouts, option-free state geometry, a 60-law counterfactual benchmark and causal interventions. In 50 held-out materials descriptions, three independently fitted Jacobian lenses reproduced concept ranks, and target-free word sets from both readouts enabled blinded identification of 9 of 10 mechanism families. A separate 72-prompt benchmark produced mechanism-specific hidden-state neighborhoods, but an exact graph audit showed that this apparent physical organization was equally explained by numerical comparison. We therefore compared otherwise identical prompts in which only the direction of the physical input was reversed, asking whether the resulting hidden-state movement followed the supplied constitutive law. These state transformations ordered direct, physically neutral and inverse laws across 60 frozen relations and correctly oriented 39 of 40 directional laws, whereas lexical controls were near chance. Bidirectional interventions shifted answer probabilities toward or away from the physically appropriate outcome across all 12 matched cases, while counterfactual state patches transferred opposing decision signals across mechanisms and answer formats. Physical relationships were therefore more visible in controlled state changes than in absolute states alone.

Structural modeling is a fundamental component of computational engineering science, in which even minor physical inconsistencies or specification violations may invalidate downstream simulations. The potential of large language models (LLMs) for automatic generation of modeling code has been demonstrated. However, non-executable or physically inconsistent outputs remain prevalent under stringent engineering constraints. A framework for physics-consistent automatic building modeling is therefore proposed, integrating domain knowledge construction, constraint-oriented model alignment, and verification-driven evaluation. CivilInstruct is introduced as a domain-specific dataset that formalizes structural engineering knowledge and constraint reasoning to enable simulation-ready model generation. A two-stage fine-tuning strategy is further employed to enforce constraint satisfaction and application programming interface compliance, substantially reducing hallucinated and non-conforming outputs. MBEval is presented as a verification-driven benchmark that evaluates executability and structural dynamics consistency through closed-loop validation. Experimental results show consistent improvements over baselines across rigorous verification metrics. Our code is available at https://github.com/Jovanqing/AutoBM.

Differentiable physics enables efficient gradient-based optimizations of neural network (NN) controllers. However, existing work typically only delivers NN controllers with limited capability and generalizability. We present a practical learning framework that outputs unified NN controllers capable of tasks with significantly improved complexity and diversity. To systematically improve training robustness and efficiency, we investigated a suite of improvements over the baseline approach, including periodic activation functions, and tailored loss functions. In addition, we find our adoption of batching and an Adam optimizer effective in training complex locomotion tasks. We evaluate our framework on differentiable mass-spring and material point method (MPM) simulations, with challenging locomotion tasks and multiple robot designs. Experiments show that our learning framework, based on differentiable physics, delivers better results than reinforcement learning and converges much faster. We demonstrate that users can interactively control soft robot locomotion and switch among multiple goals with specified velocity, height, and direction instructions using a unified NN controller trained in our system. Code is available at https://github.com/erizmr/Complex-locomotion-skill-learning-via-differentiable-physics.

Molecular dynamics (MD) simulations model the motion of proteins between conformational states, but crossing free energy barriers and sampling multiple thermodynamic conditions remain computationally costly. We recently introduced MD-LLM-1, which showed that language models can generate conformational trajectories at lower cost, but required a separate model for each protein and did not explicitly model thermodynamics or kinetics. Here we introduce MD-LLM-2, a transferable language model that generates trajectories conditioned on sequence, temperature and molecular history. Because each step defines a normalized distribution over structural tokens, the model assigns an explicit likelihood to every generated or simulated trajectory. Trained across mdCATH domains, MD-LLM-2 reproduces the median radius of gyration of MD within 1 Angstrom in 10 of 12 unseen domains, predicts reduced Trp-cage compaction at higher temperature, and generates L99A T4 lysozyme trajectories that reach published transition-region backbone structures. In alanine dipeptide simulations, conditioning on a torsional scaling parameter λ predicts basin populations at unseen couplings with a mean absolute error of 0.09 versus 0.35 for MBAR, and first-passage probabilities with an error of 0.08 versus 0.16 for a reversible Markov state model. Frame-isoentropic sampling further limits the accumulation of errors during autoregressive trajectory generation. Together, these results extend MD-LLM from protein-specific trajectory generation to transferable, physically conditioned modelling with explicit path likelihoods, and show that the framework can predict equilibrium populations for force-field parameters not seen during training, with an initial indication that first-passage kinetics can also be captured.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

Crash simulation is a cornerstone of modern vehicle development because it reduces the need for costly physical prototypes, accelerates safety-driven design iteration, and increasingly supports virtual testing workflows. At the same time, modeling structural crash mechanics remains exceptionally challenging: the response is governed by nonlinear contact, large deformation, material plasticity, failure, and complex multi-body interactions evolving over space and time on high-resolution finite-element meshes. In this work, we introduce CarCrashNet, a public high-fidelity open-source benchmark for data-driven structural crash simulation. CarCrashNet combines component-scale and full-vehicle simulations in a multi-modal format, including more than 14{,}000 bumper-beam pole-impact simulations with varying geometry, materials, and boundary conditions, together with 825 full-vehicle crash simulations built from three industry-standard vehicle models of increasing structural complexity: Dodge Neon, Toyota Yaris, and Chevrolet Silverado. To establish the reliability of the benchmark, we validate our open-source finite-element workflow based on OpenRadioss against both experimental crash data and the commercial solver Ansys LS-DYNA. We also introduce CrashSolver, a machine-learning model designed for full-vehicle crash prediction from high-resolution finite-element crash data. We further perform extensive benchmarking across the released datasets and evaluate CrashSolver against state-of-the-art geometric deep learning and transformer-based neural solvers. Our results position CarCrashNet as a foundation for reproducible research in structural simulation, crashworthiness modeling, and AI-driven virtual crash testing. The dataset is available at https://github.com/Mohamedelrefaie/CarCrashNet.

We introduce Tadpole, a novel foundation model for three-dimensional partial differential equations (PDEs) that addresses key challenges in transferability, scalability to high dimensionality, and multi-functionality. Tadpole is pre-trained as an autoencoder on synthetic 3D PDE data generated by an efficient online data-generation framework. This enables large-scale, diverse training without storage or I/O overhead, demonstrated by scaling to an equivalent of hundreds of terabytes of training data. By autoencoding single-channel spatial crops, Tadpole learns rich and transferable representations across heterogeneous physical systems with varying numbers of state variables and spatial resolutions. Although pre-trained solely as an autoencoder, Tadpole can be efficiently applied for multiple downstream tasks beyond reconstruction, including dynamics learning and generative modeling. For dynamics learning, we propose a novel parameter-efficient fine-tuning strategy that integrates low-rank adaptation, latent-space transformations, and reintroduced skip connections, achieving accurate temporal modeling with a minimal number of trainable parameters. Tadpole demonstrates strong fine-tuning performance across various downstream tasks, highlighting its versatility and effectiveness as a foundation model for 3D PDE learning. Source code and pre-trained weights of Tadpole are available at https://github.com/tum-pbs/tadpole

Dislocation model of the supersolid state of ^4He was proposed in 1987 by one of the authors of the review. The model obtained strong support by numerous experimental and theoretical investigations from 2007 to date. In these investigations the validity of the idea put forward in 1987 was confirmed, and new conceptions of superclimb of dislocations and of the giant isochoric compressibility or the syringe effect were proposed. In this paper we review main achievements of theoretical and experimental studies of dislocation-induced supersolid and present current understanding of this phenomenon.

In this paper, we examine the thermodynamic behavior of a quantum harmonic oscillator with a position-dependent mass (PDM), where spatial inhomogeneity is modeled through a deformation parameter α. Based on the exact energy spectrum, we explore the resulting thermodynamic quantities and superstatistics. Our findings reveal that increasing α leads to a decrease in entropy and specific heat, reflecting a confinement-induced reduction in the number of accessible states. The partition function and free energy exhibit smooth behavior across all parameter regimes, indicating the absence of critical phase transitions. This study underscores the influence of mass deformation on quantum thermal responses and demonstrates that, while the overall thermodynamic trends are consistent with those reported in the literature, certain distinctive features emerge due to the specific form of the deformation.

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis can be used when systems undergo low-frequency vibrations. In the case of fast dynamics and wave propagation, we investigate a random generator of boundary conditions for fast submodels by using machine learning. We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant. Physics-informed neural networks is a possible choice for a data-driven method to replace linear modal analysis. An architecture that support a random component is necessary for the construction of the stochastic model of the physical system for non-parametric uncertainties, since the goal is to learn the underlying probabilistic distribution of uncertainty in the data. Generative Adversarial Networks (GANs) are suited for such applications, where the Wasserstein-GAN with gradient penalty variant offers improved convergence results for our problem. The objective of our approach is to train a GAN on data from a finite element method code (Fenics) so as to extract stochastic boundary conditions for faster finite element predictions on a submodel. The submodel and the training data have both the same geometrical support. It is a zone of interest for uncertainty quantification and relevant to engineering purposes. In the exploitation phase, the framework can be viewed as a randomized and parametrized simulation generator on the submodel, which can be used as a Monte Carlo estimator.

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

We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local parametrization that uses a four-point computational stencil, which has several advantages over globally coupled parametrizations. We demonstrate numerically that our method improves energy balance in long-term turbulent simulations and also accurately reproduces individual solutions. The neural network parametrization can be easily combined with flux limiting to reduce oscillations near shocks. More importantly, our method provides reliable parametrizations, even in dynamical regimes that are not included in the training data.

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

Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. The majority of existing TO approaches leverage numerical solvers for design evaluations during the optimization and hence have a nested nature and rely on discretizing the design variables. Contrary to these approaches, herein we develop a new class of TO methods based on the framework of Gaussian processes (GPs) whose mean functions are parameterized via deep neural networks. Specifically, we place GP priors on all design and state variables to represent them via parameterized continuous functions. These GPs share a deep neural network as their mean function but have as many independent kernels as there are state and design variables. We estimate all the parameters of our model in a single for loop that optimizes a penalized version of the performance metric where the penalty terms correspond to the state equations and design constraints. Attractive features of our approach include (1) having a built-in continuation nature since the performance metric is optimized at the same time that the state equations are solved, and (2) being discretization-invariant and accommodating complex domains and topologies. To test our method against conventional TO approaches implemented in commercial software, we evaluate it on four problems involving the minimization of dissipated power in Stokes flow. The results indicate that our approach does not need filtering techniques, has consistent computational costs, and is highly robust against random initializations and problem setup.

Asymptotic Safety provides a promising framework for the quantization of Scalar-Tensor theories as non-perturbatively renormalizable quantum field theories. Over the past years, growing evidence has accumulated for the existence of non-trivial renormalization group fixed points in a variety of Scalar-Tensor models. In this work, we investigate the robustness of these fixed points under significant modifications of the computational setup. In particular, we employ a gauge condition that explicitly depends on the dynamical scalar field, going beyond a mere gauge-parameter deformation of the standard linear covariant gauges commonly used in the literature. Exploring different field parameterizations, we identify fixed points belonging to the Gaussian Matter class in four spacetime dimensions that are consistent with previous studies. The real part of the critical exponents associated with the scalar-field mass and the non-minimal scalar-curvature coupling turn out to have very small absolute value. We provide a comprehensive exploration of how the anomalous dimension of the scalar field and field parameterization impact those critical exponents showing that fixed-point candidates with two or four relevant directions emerge.

Spring-based actuators in legged locomotion provide energy-efficiency and improved performance, but increase the difficulty of controller design. While previous work has focused on extensive modeling and simulation to find optimal controllers for such systems, we propose to learn model-free controllers directly on the real robot. In our approach, gaits are first synthesized by central pattern generators (CPGs), whose parameters are optimized to quickly obtain an open-loop controller that achieves efficient locomotion. Then, to make this controller more robust and further improve the performance, we use reinforcement learning to close the loop, to learn corrective actions on top of the CPGs. We evaluate the proposed approach on the DLR elastic quadruped bert. Our results in learning trotting and pronking gaits show that exploitation of the spring actuator dynamics emerges naturally from optimizing for dynamic motions, yielding high-performing locomotion, particularly the fastest walking gait recorded on bert, despite being model-free. The whole process takes no more than 1.5 hours on the real robot and results in natural-looking gaits.

Directed energy deposition (DED) produces complex thermo-mechanical responses that can lead to distortion and reduced dimensional accuracy of a manufactured part. Thermo-mechanical finite element simulations are widely used to estimate these effects, but their computational cost and the complexity of accurately capturing DED physics limit their use in design iteration and process optimization. This paper introduces FLARE (Field Prediction via Linear Affine Reconstruction in wEight-space), a data-efficient surrogate modeling framework for predicting post-cooling displacement fields in DED from geometric and process parameters. We develop a predefined-geometry DED simulation workflow using an open-source finite element framework and generate a dataset of simulations with varying geometry, laser power, and deposition velocity. Each simulation provides full-field displacement, stress, strain, and temperature data throughout the manufacturing process. FLARE encodes each simulation as an implicit neural field and regularizes the corresponding neural-network weights so that they follow the affine structure of the input parameter space. This enables prediction of unseen parameter combinations by reconstructing network weights through affine mixing of training examples. On this DED benchmark, the method shows improved accuracy compared to baseline methods in both in-distribution and extrapolation settings. Although the present study focuses on DED displacement prediction, the proposed affine weight-space reconstruction framework offers a promising approach for data-efficient surrogate modeling of physical fields.

Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields.Neural networks are well-suited for PDE parameter estimation due to their capability to model function-to-function space transformations. While existing benchmarks of machine learning methods for PDEs primarily focus on the forward problem, there are no similar comprehensive studies and benchmark datasets on PDE inverse problems, i.e., mapping solution fields to underlying physical parameters. We fill this gap by introducing PDEInvBench, a comprehensive benchmark dataset consisting of numerical simulations for both time-dependent and time-independent PDEs across a wide range of physical behaviors and parameters. Our dataset includes evaluation splits that assess performance in both in-distribution and various out-of-distribution settings. Using our benchmark dataset, we comprehensively explore the design space of neural networks for PDE inverse problems along three key dimensions: (1) optimization procedures, analyzing the role of supervised, self-supervised, and test-time training objectives on performance, (2) problem representations, where we study the value of architectural choices with different inductive biases and various conditioning strategies, and (3) scaling, which we perform with respect to both model and data size. Our experiments reveal several practical insights: 1) neural networks perform best with a two-stage training procedure: initial supervision with PDE parameters followed by test-time fine-tuning using the PDE residual, 2) incorporating PDE derivatives as input features consistently improves accuracy, and 3) increasing the diversity of initial conditions in the training data yields greater performance gains than expanding the range of PDE parameters. We make our dataset and codebase publicly available.

The temperature parameter plays a profound role during training and/or inference with large foundation models (LFMs) such as large language models (LLMs) and CLIP models. Particularly, it adjusts the logits in the softmax function in LLMs, which is crucial for next token generation, and it scales the similarities in the contrastive loss for training CLIP models. A significant question remains: Is it viable to learn a neural network to predict a personalized temperature of any input data for enhancing LFMs"? In this paper, we present a principled framework for learning a small yet generalizable temperature prediction network (TempNet) to improve LFMs. Our solution is composed of a novel learning framework with a robust loss underpinned by constrained distributionally robust optimization (DRO), and a properly designed TempNet with theoretical inspiration. TempNet can be trained together with a large foundation model from scratch or learned separately given a pretrained foundation model. It is not only useful for predicting personalized temperature to promote the training of LFMs but also generalizable and transferable to new tasks. Our experiments on LLMs and CLIP models demonstrate that TempNet greatly improves the performance of existing solutions or models, e.g. Table 1. The code to reproduce the experimental results in this paper can be found at https://github.com/zhqiu/TempNet.

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

The relationship between material properties and independent variables such as temperature, external field or time, is usually represented by a curve or surface in a multi-dimensional space. Determining such a curve or surface requires a series of experiments or calculations which are often time and cost consuming. A general strategy uses an appropriate utility function to sample the space to recommend the next optimal experiment or calculation within an active learning loop. However, knowing what the optimal sampling strategy to use to minimize the number of experiments is an outstanding problem. We compare a number of strategies based on directed exploration on several materials problems of varying complexity using a Kriging based model. These include one dimensional curves such as the fatigue life curve for 304L stainless steel and the Liquidus line of the Fe-C phase diagram, surfaces such as the Hartmann 3 function in 3D space and the fitted intermolecular potential for Ar-SH, and a four dimensional data set of experimental measurements for BaTiO3 based ceramics. We also consider the effects of experimental noise on the Hartmann 3 function. We find that directed exploration guided by maximum variance provides better performance overall, converging faster across several data sets. However, for certain problems, the trade-off methods incorporating exploitation can perform at least as well, if not better than maximum variance. Thus, we discuss how the choice of the utility function depends on the distribution of the data, the model performance and uncertainties, additive noise as well as the budget.

Using absorbance measurements through a Couette cell containing an emulsion of buoyant droplets, volume fraction profiles are measured at various shear rates. These viscous resuspension experiments allow a direct determination of the normal stress in the vorticity direction in connection with the suspension balance model that has been developed for suspensions of solid particles. The results unambigously show that the normal viscosity responsible for the shear-induced migration of the droplets is independant on the capillary number, implying that particle deformation does not play a great role. It is similar to that of rigid particles at volume fractions below 40\% but much smaller at higher ones.

The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator optimization where non-axisymmetric magnetic fields with a large parameter space are optimized to satisfy certain performance criteria. However, optimization is still required to find configurations with properties such as low elongation, high rotational transform, finite plasma beta, and good fast particle confinement. In this work, we train a machine learning model to construct configurations with favorable confinement properties by finding a solution to the inverse design problem, that is, obtaining a set of model input parameters for given desired properties. Since the solution of the inverse problem is non-unique, a probabilistic approach, based on mixture density networks, is used. It is shown that optimized configurations can be generated reliably using this method.

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM) mitigates this cost by evolving low-dimensional latent representations of the underlying system. While neural ROMs enable querying solutions from latent states at arbitrary spatial points, their latent states typically represent the global domain and struggle to capture localized, highly dynamic behaviors such as fluids. We propose a sampling-based reduction framework that evolves Lagrangian systems directly in physical space over the particles themselves, reducing the number of active degrees of freedom via data-driven neural PDE operators. To enable querying at arbitrary spatial locations, we introduce a learnable kernel parameterization that uses local spatial information from time-evolved sample particles to infer the underlying solution manifold. Empirically, our approach achieves a 6.6x to 32x reduction in input dimensionality while maintaining high-fidelity evaluations across diverse Lagrangian regimes, including fluid flows, granular media, and elastoplastic dynamics. We refer to this framework as GIOROM (Geometry-Informed Reduced-Order Modeling). All code and data are available at: https://github.com/HrishikeshVish/GIOROM

Predicting flows that occur both through and around porous bodies is challenging due to coupled physics across fluid and porous regions and the need to generalize across diverse geometries and boundary conditions. We address this problem using two Physics Informed learning approaches: Physics Informed PointNets (PIPN) and Physics Informed Geometry Aware Neural Operator (P-IGANO). We enforce the incompressible Navier Stokes equations in the free-flow region and a Darcy Forchheimer extension in the porous region within a unified loss and condition the networks on geometry and material parameters. Datasets are generated with OpenFOAM on 2D ducts containing porous obstacles and on 3D windbreak scenarios with tree canopies and buildings. We first verify the pipeline via the method of manufactured solutions, then assess generalization to unseen shapes, and for PI-GANO, to variable boundary conditions and parameter settings. The results show consistently low velocity and pressure errors in both seen and unseen cases, with accurate reproduction of the wake structures. Performance degrades primarily near sharp interfaces and in regions with large gradients. Overall, the study provides a first systematic evaluation of PIPN/PI-GANO for simultaneous through-and-around porous flows and shows their potential to accelerate design studies without retraining per geometry.

Studies show that the model-independent, fully non-perturbative covariant cosmographic approach is suitable for analyzing the local Universe (zlesssim 0.1). However, accurately characterizing large and inhomogeneous mass distributions requires the fourth-order term in the redshift expansion of the covariant luminosity distance d_L(z,n). We calculate the covariant snap parameter S and its spherical harmonic multipole moments using the matter expansion tensor and the evolution equations for lightray bundles. The fourth-order term adds 36 degrees of freedom, since the highest independent multipole of the snap is the 32-pole (dotriacontapole) (ell=5). Including this term helps to de-bias estimations of the covariant deceleration parameter. Given that observations suggest axially symmetric anisotropies in the Hubble diagram for z lesssim 0.1 and theory shows that only a subset of multipoles contributes to the signal, we demonstrate that only 12 degrees of freedom are needed for a model-independent description of the local universe. We use an analytical axisymmetric model of the local Universe, with data that matches the Zwicky Transient Facility survey, in order to provide a numerical example of the amplitude of the snap multipoles and to forecast precision.

We present formulation and open-source tools to achieve in-material model predictive control of sensor/actuator systems using learned forward kinematics and on-device computation. Microcontroller units (MCUs) that compute the prediction and control task while colocated with the sensors and actuators enable in-material untethered behaviors. In this approach, small parameter size neural network models learn forward kinematics offline. Our open-source compiler, nn4mc, generates code to offload these predictions onto MCUs. A Newton-Raphson solver then computes the control input in real time. We first benchmark this nonlinear control approach against a PID controller on a mass-spring-damper simulation. We then study experimental results on two experimental rigs with different sensing, actuation and computational hardware: a tendon-based platform with embedded LightLace sensors and a HASEL-based platform with magnetic sensors. Experimental results indicate effective high-bandwidth tracking of reference paths (greater than or equal to 120 Hz) with a small memory footprint (less than or equal to 6.4% of flash memory). The measured path following error does not exceed 2mm in the tendon-based platform. The simulated path following error does not exceed 1mm in the HASEL-based platform. The mean power consumption of this approach in an ARM Cortex-M4f device is 45.4 mW. This control approach is also compatible with Tensorflow Lite models and equivalent on-device code. In-material intelligence enables a new class of composites that infuse autonomy into structures and systems with refined artificial proprioception.

System identification from videos aims to recover object geometry and governing physical laws. Existing methods integrate differentiable rendering with simulation but rely on predefined material priors, limiting their ability to handle unknown ones. We introduce MASIV, the first vision-based framework for material-agnostic system identification. Unlike existing approaches that depend on hand-crafted constitutive laws, MASIV employs learnable neural constitutive models, inferring object dynamics without assuming a scene-specific material prior. However, the absence of full particle state information imposes unique challenges, leading to unstable optimization and physically implausible behaviors. To address this, we introduce dense geometric guidance by reconstructing continuum particle trajectories, providing temporally rich motion constraints beyond sparse visual cues. Comprehensive experiments show that MASIV achieves state-of-the-art performance in geometric accuracy, rendering quality, and generalization ability.

Recent advances in physical 3D generation have enabled visually faithful assets with simulatable mechanical behavior. However, existing methods provide limited control over material behavior beyond appearance-based inference and struggle to estimate physical properties from complex interactions between objects and semantic parts. Therefore, we present PhysForge, a Video Diffusion Model (VDM)-based framework for addressing these challenges, comprising two complementary modules for material-controllable physical fitting and componentlevel interaction modeling. The first, PhysFit, leverages material-conditioned VDM dynamics as references for physical-property fitting, introducing windowed fitting to focus on material-revealing interactions and Hallucinated Forcing to disentangle nonphysical motion hallucinated by the VDM from material responses. The second, PhysComp decomposes complex interactions into individual objects and semantic components, enabling their physical parameters to be optimized independently and flexibly composed for joint simulation. Experiments on PhysAssets and Google Scanned Objects demonstrate that, compared with existing methods, PhysForge provides stronger control over material-dependent physical responses while supporting component-level physical modeling for complex interactions. It achieves the best CLIP and physical controllability scores on both common and uncommon materials, with qualitative comparisons, component-level ablations, and a user study further supporting these improvements. Our project page is available at https://masterwanna.github.io/PhysForge.html .

Global climate models parameterize a range of atmospheric-oceanic processes like gravity waves, clouds, moist convection, and turbulence that cannot be sufficiently resolved. These subgrid-scale closures for unresolved processes are a leading source of model uncertainty. Here, we present a new approach to developing machine learning parameterizations of small-scale climate processes by fine-tuning a pre-trained AI foundation model (FM). FMs are largely unexplored in climate research. A pre-trained encoder-decoder from a 2.3 billion parameter FM (NASA and IBM Research's Prithvi WxC) -- which contains a latent probabilistic representation of atmospheric evolution -- is fine-tuned (or reused) to create a deep learning parameterization for atmospheric gravity waves (GWs). The parameterization captures GW effects for a coarse-resolution climate model by learning the fluxes from an atmospheric reanalysis with 10 times finer resolution. A comparison of monthly averages and instantaneous evolution with a machine learning model baseline (an Attention U-Net) reveals superior predictive performance of the FM parameterization throughout the atmosphere, even in regions excluded from pre-training. This performance boost is quantified using the Hellinger distance, which is 0.11 for the baseline and 0.06 for the fine-tuned model. Our findings emphasize the versatility and reusability of FMs, which could be used to accomplish a range of atmosphere- and climate-related applications, leading the way for the creation of observations-driven and physically accurate parameterizations for more earth-system processes.

We construct an odd smooth initial density for the unforced incompressible porous media (IPM) equation on mathbb T^2 whose solution develops a finite-time blowup. The components partial_{x_2}ρ(t,0) and partial_{x_1}u_1(t,0) tend to +infty as the maximal smooth existence time is approached, while the density and velocity remain bounded in L^2. Starting from a stationary solution, we iterate the angular amplification of localized oscillations with rapidly growing frequencies, adapting the mechanism of Córdoba and Martínez-Zoroa [7] for forced IPM. Each perturbation is constructed from time zero and creates the geometry configuration for the next iteration stage. A one-sided upper bound for the pressure Hessian is applied to control backward preparation and initial perturbations, following an idea from the Euler construction of OpenAI [14].

We present 3D DEM simulations of bidisperse granular packings to investigate their jamming densities, phi_J, and dimensionless bulk moduli, K, as a function of the size ratio, delta, and the concentration of small particles, X_{mathrm S}. We determine the partial and total bulk moduli for each packing and report the jamming transition diagram, i.e., the density or volume fraction marking both the first and second transitions of the system. At a large enough size difference, e.g., delta le 0.22, X^{*}_{mathrm S} divides the diagram with most small particles either non-jammed or jammed jointly with large ones. We find that the bulk modulus K jumps at X^{*}_{mathrm S}(delta = 0.15) approx 0.21, at the maximum jamming density, where both particle species mix most efficiently, while for X_{mathrm S} < X^{*}_{mathrm S} K is decoupled in two scenarios as a result of the first and second jamming transition. Along the second transition, K rises relative to the values found at the first transition, however, is still small compared to K at X^{*}_{mathrm S}. While the first transition is sharp, the second is smooth, carried by small-large interactions, while the small-small contacts display a transition. This demonstrates that for low enough delta and X_{mathrm S}, the jamming of small particles indeed impacts the internal resistance of the system. Our new results will allow tuning the bulk modulus K or other properties, such as the wave speed, by choosing specific sizes and concentrations based on a better understanding of whether small particles contribute to the jammed structure or not, and how the micromechanical structure behaves at either transition.

This review presents the elastic theory of low-dimensional (one- and two-dimensional) continua and its applications in bio- and nano-structures. First, the curve and surface theory, as the geometric representation of the low-dimensional continua, is briefly described through Cartan moving frame method. The elastic theory of Kirchhoff rod, Helfrich rod, bending-soften rod, fluid membrane, and solid shell is revisited. Secondly, the application and availability of the elastic theory of low-dimensional continua in bio-structures, including short DNA rings, lipid membranes, and cell membranes, are discussed. The kink stability of short DNA rings is addressed by using the theory of Kirchhoff rod, Helfrich rod, and bending-soften rod. The lipid membranes obey the theory of fluid membrane. A cell membrane is simplified as a composite shell of lipid bilayer and membrane skeleton, which is a little similar to the solid shell. It is found that the membrane skeleton enhances highly the mechanical stability of cell membranes. Thirdly, the application and availability of the elastic theory of low-dimensional continua in nano-structures, including graphene and carbon nanotubes, are discussed. A revised Lenosky lattice model is proposed based on the local density approximation. Its continuum form up to the second order terms of curvatures and strains is the same as the free energy of 2D solid shells. Several typical mechanical properties of carbon nanotubes are revisited and investigated based on this continuum form. It is possible to avoid introducing the controversial concepts, the Young's modulus and thickness of graphene and single-walled carbon nanotubes, with this continuum form.

Since loose-fitting clothing contains dynamic modes that have proven to be difficult to predict via neural networks, we first illustrate how to coarsely approximate these modes with a real-time numerical algorithm specifically designed to mimic the most important ballistic features of a classical numerical simulation. Although there is some flexibility in the choice of the numerical algorithm used as a proxy for full simulation, it is essential that the stability and accuracy be independent from any time step restriction or similar requirements in order to facilitate real-time performance. In order to reduce the number of degrees of freedom that require approximations to their dynamics, we simulate rigid frames and use skinning to reconstruct a rough approximation to a desirable mesh; as one might expect, neural-network-based skinning seems to perform better than linear blend skinning in this scenario. Improved high frequency deformations are subsequently added to the skinned mesh via a quasistatic neural network (QNN). In contrast to recurrent neural networks that require a plethora of training data in order to adequately generalize to new examples, QNNs perform well with significantly less training data.

Parameterized tight-binding models fit to first principles calculations can provide an efficient and accurate quantum mechanical method for predicting properties of molecules and solids. However, well-tested parameter sets are generally only available for a limited number of atom combinations, making routine use of this method difficult. Furthermore, most previous models consider only simple two-body interactions, which limits accuracy. To tackle these challenges, we develop a density functional theory database of nearly one million materials, which we use to fit a universal set of tight-binding parameters for 65 elements and their binary combinations. We include both two-body and three-body effective interaction terms in our model, plus self-consistent charge transfer, enabling our model to work for metallic, covalent, and ionic bonds with the same parameter set. To ensure predictive power, we adopt a learning framework where we repeatedly test the model on new low energy crystal structures and then add them to the fitting dataset, iterating until predictions improve. We distribute the materials database and tools developed in this work publicly.

Design of neural networks that incorporate symmetry is crucial for geometric deep learning. Central to this effort is the development of invariant and equivariant operations. This works presents a systematic method for constructing valid invariant and equivariant operations. It can handle inputs and outputs in the form of Cartesian tensors with different rank, as well as spherical tensors with different types. In addition, our method features a graphical representation utilizing the symmetric tensor network, which simplifies both the proofs and constructions related to invariant and equivariant functions. We also apply this approach to design the equivariant interaction message for the geometry graph neural network, and equivariant machine learning model to learn the constitutive law of materials.

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

Asphalt concrete's (AC) durability and maintenance demands are strongly influenced by its fatigue life. Traditional methods for determining this characteristic are both resource-intensive and time-consuming. This study employs artificial neural networks (ANNs) to predict AC fatigue life, focusing on the impact of strain level, binder content, and air-void content. Leveraging a substantial dataset, we tailored our models to effectively handle the wide range of fatigue life data, typically represented on a logarithmic scale. The mean square logarithmic error was utilized as the loss function to enhance prediction accuracy across all levels of fatigue life. Through comparative analysis of various hyperparameters, we developed a machine-learning model that captures the complex relationships within the data. Our findings demonstrate that higher binder content significantly enhances fatigue life, while the influence of air-void content is more variable, depending on binder levels. Most importantly, this study provides insights into the intricacies of using ANNs for modeling, showcasing their potential utility with larger datasets. The codes developed and the data used in this study are provided as open source on a GitHub repository, with a link included in the paper for full access.

We propose a reduced-space elasto-dynamic solver that is well suited for augmenting rigged character animations with secondary motion. At the core of our method is a novel deformation subspace based on Linear Blend Skinning that overcomes many of the shortcomings prior subspace methods face. Our skinning subspace is parameterized entirely by a set of scalar weights, which we can obtain through a small, material-aware and rig-sensitive generalized eigenvalue problem. The resulting subspace can easily capture rotational motion and guarantees that the resulting simulation is rotation equivariant. We further propose a simple local-global solver for linear co-rotational elasticity and propose a clustering method to aggregate per-tetrahedra non-linear energetic quantities. The result is a compact simulation that is fully decoupled from the complexity of the mesh.