A matrix-free, GPU-compatible PyTorch implementation of phase-field fracture with explicit dynamics, custom differentiable implicit damage solve, benchmarks on dynamic and quasi-static cases, and inverse recovery of fracture energy G_c via L-BFGS.
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representative citing papers
Derives three-term singularity asymptotics for surface-sourced Neumann Green's function and implements high-order BIE with Duffy patches to compute the regular part on arbitrary smooth surfaces, validated on spheres and spheroids.
The EXTRA method enables accurate 3D magneto-thermal FE simulations of large-scale NI HTS magnets by explicitly resolving critical turns while homogenizing others, reducing computation time by up to 13x on benchmarks.
SPEC CPU 2026 presents a new benchmark suite using open-source apps, expanded multithreading, and Rolling-Round-Robin Rate to address gaps in evaluating heterogeneous multiprogrammed CPU performance.
New coercive diffuse domain methods for Dirichlet conditions derived from mixed formulations and Nitsche's approach, with coercivity proofs and numerical tests showing improved accuracy on Navier-Stokes benchmarks.
A constrained LLM front-end for FEniCS multi-physics simulations dispatches to human-written templates and achieves 100% valid parses plus 90-100% geometry success on benchmarks while avoiding LLM-generated solver code.
PDE-Agents shows a LangGraph-orchestrated multi-agent LLM framework with GraphRAG that reaches 100% task success and perfect material fidelity on novel materials in ablation tests, with 97.8% success across 1369 production runs.
Presents and verifies a surface contact approximation derived from the thin shell approximation for efficient magneto-thermal FEA of no-insulation HTS coils, showing robustness advantages over thickness-dependent TSA in pancake coil simulations.
EquiNO with Q-DEIM creates reduced-order physics-informed surrogates for 3D hyperelastic RVEs that enforce equilibrium and periodicity by construction, achieve 10^3 speedups, and accurately interpolate and extrapolate stresses from few snapshots.
A continuous 50-nm Permalloy film on 400-nm-period nanopyramid templates forms a 2D magnonic crystal exhibiting a complete tunable in-plane band gap and strongly localized flat-band modes due to curvature-induced demagnetizing fields.
DeepONet learns the operator from signed distance functions of arbitrary 2D scatterer geometries to the resulting scattered fields for the Helmholtz equation, generalizing to unseen shapes as a surrogate for FEM.
EMSL groups material points into clusters, samples a reference strain per cluster once per increment, and computes a linearised stress estimate from the reference tangent and POD strain modes, yielding an affine reduced system that requires no iterations online and Pareto-dominates prior strain-cubc
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
mLaSDI uses multi-stage residual decoder training with periodic activations to recover high-frequency details in latent space dynamics identification, yielding lower reconstruction and prediction errors than standard LaSDI for PDEs.
Develops an evolving finite element method for parabolic PDEs with evolving interfaces, derives a suitable weak formulation, proves optimal error bounds for isoparametric elements of arbitrary order, and verifies convergence numerically.
Simulations using a Swelling & Random Migration algorithm and finite element homogenization show clustered fiber distributions increase transverse stiffness by up to 20% but reduce tensile strength compared to equilibrium distributions, with mean nearest neighbor distance linearly predicting both pr
A multi-agent LLM framework autonomously completes the full computational mechanics pipeline from a photograph to a code-compliant engineering report on a steel L-bracket example.
Shape optimization of Maxwell eigenvalues via adjoint sensitivities on a reference domain, solved with a damped inverse BFGS method and mixed finite elements.
jNO introduces a unified JAX tracing system for data-driven and physics-informed neural operator training that compiles domains, residuals, losses, and diagnostics into one pipeline.
Smoothing iterations on finite element solutions in an enriched space produce superconvergent approximations for symmetric positive definite problems.
The paper reviews recent developments and unresolved challenges in cardiac mechanics modeling, arguing that identifying essential complexities versus safe simplifications is key to clinical translation.
citing papers explorer
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A matrix-free, differentiable PyTorch solver for phase-field fracture: Formulation, benchmarks, and inverse analysis
A matrix-free, GPU-compatible PyTorch implementation of phase-field fracture with explicit dynamics, custom differentiable implicit damage solve, benchmarks on dynamic and quasi-static cases, and inverse recovery of fracture energy G_c via L-BFGS.
-
The three dimensional Neumann Green's function for general surfaces: singular asymptotics and boundary integral methods
Derives three-term singularity asymptotics for surface-sourced Neumann Green's function and implements high-order BIE with Duffy patches to compute the regular part on arbitrary smooth surfaces, validated on spheres and spheroids.
-
Explicit Turn Resolution with Anisotropic Homogenisation for Efficient 3D Magneto-Thermal Finite-Element Simulation of Large-Scale No-Insulation HTS Magnets
The EXTRA method enables accurate 3D magneto-thermal FE simulations of large-scale NI HTS magnets by explicitly resolving critical turns while homogenizing others, reducing computation time by up to 13x on benchmarks.
-
SPEC CPU: The Next Generation
SPEC CPU 2026 presents a new benchmark suite using open-source apps, expanded multithreading, and Rolling-Round-Robin Rate to address gaps in evaluating heterogeneous multiprogrammed CPU performance.
-
Diffuse Domain Methods with Dirichlet Boundary Conditions
New coercive diffuse domain methods for Dirichlet conditions derived from mixed formulations and Nitsche's approach, with coercivity proofs and numerical tests showing improved accuracy on Navier-Stokes benchmarks.
-
A Constrained Natural-Language Interface for Variational Multi-Physics Finite Element Simulations in FEniCS
A constrained LLM front-end for FEniCS multi-physics simulations dispatches to human-written templates and achieves 100% valid parses plus 90-100% geometry success on benchmarks while avoiding LLM-generated solver code.
-
PDE-Agents: An LLM-Orchestrated Multi-Agent Framework for Automated Finite Element Simulations with Knowledge Graph-Augmented Reasoning
PDE-Agents shows a LangGraph-orchestrated multi-agent LLM framework with GraphRAG that reaches 100% task success and perfect material fidelity on novel materials in ablation tests, with 97.8% success across 1369 production runs.
-
Surface Contact Approximation for Magneto-Thermal Finite Element Analysis of No-Insulation HTS Coils
Presents and verifies a surface contact approximation derived from the thin shell approximation for efficient magneto-thermal FEA of no-insulation HTS coils, showing robustness advantages over thickness-dependent TSA in pancake coil simulations.
-
Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics
EquiNO with Q-DEIM creates reduced-order physics-informed surrogates for 3D hyperelastic RVEs that enforce equilibrium and periodicity by construction, achieve 10^3 speedups, and accurately interpolate and extrapolate stresses from few snapshots.
-
Sculpting Spin-Wave Landscapes via Curvature of 2D Magnonic Crystals
A continuous 50-nm Permalloy film on 400-nm-period nanopyramid templates forms a 2D magnonic crystal exhibiting a complete tunable in-plane band gap and strongly localized flat-band modes due to curvature-induced demagnetizing fields.
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Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries
DeepONet learns the operator from signed distance functions of arbitrary 2D scatterer geometries to the resulting scattered fields for the Helmholtz equation, generalizing to unseen shapes as a surrogate for FEM.
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Empirical Material Sampling and Linearisation -- A Simple and Efficient Strain-Space Model Order Reduction Approach for Computational Homogenisation in Large-Deformation Hyperelasticity
EMSL groups material points into clusters, samples a reference strain per cluster once per increment, and computes a linearised stress estimate from the reference tangent and POD strain modes, yielding an affine reduced system that requires no iterations online and Pareto-dominates prior strain-cubc
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Numerical approximation of the Koopman-von Neumann equation: Operator learning and quantum computing
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
-
mLaSDI: Multi-stage latent space dynamics identification
mLaSDI uses multi-stage residual decoder training with periodic activations to recover high-frequency details in latent space dynamics identification, yielding lower reconstruction and prediction errors than standard LaSDI for PDEs.
-
Evolving finite elements for advection diffusion with an evolving interface
Develops an evolving finite element method for parabolic PDEs with evolving interfaces, derives a suitable weak formulation, proves optimal error bounds for isoparametric elements of arbitrary order, and verifies convergence numerically.
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Modelling the effect of fiber distribution on the transverse mechanical characteristics of unidirectionally reinforced continuous-fiber composite
Simulations using a Swelling & Random Migration algorithm and finite element homogenization show clustered fiber distributions increase transverse stiffness by up to 20% but reduce tensile strength compared to equilibrium distributions, with mean nearest neighbor distance linearly predicting both pr
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From Perception to Autonomous Computational Modeling: A Multi-Agent Approach
A multi-agent LLM framework autonomously completes the full computational mechanics pipeline from a photograph to a code-compliant engineering report on a steel L-bracket example.
-
Numerical Eigenvalue Optimization by Shape-Variations for Maxwell's Eigenvalue Problem
Shape optimization of Maxwell eigenvalues via adjoint sensitivities on a reference domain, solved with a damped inverse BFGS method and mixed finite elements.
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jNO: A JAX Library for Neural Operator and Foundation Model Training
jNO introduces a unified JAX tracing system for data-driven and physics-informed neural operator training that compiles domains, residuals, losses, and diagnostics into one pipeline.
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Superconvergence in finite element method by smoothing
Smoothing iterations on finite element solutions in an enriched space produce superconvergent approximations for symmetric positive definite problems.
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Cardiac mechanics modeling: recent developments and current challenges
The paper reviews recent developments and unresolved challenges in cardiac mechanics modeling, arguing that identifying essential complexities versus safe simplifications is key to clinical translation.