Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics

• URL: http://arxiv.org/abs/2605.07738v1
• Date: Fri, 08 May 2026 13:46:28 GMT
• Title: Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics
• Abstract summary: Physics-informed operator learning is an attractive candidate for surrogate modeling of microstructures.<n>Q-DEIM reduces the per-step training cost by roughly three orders of magnitude relative to full-field loss evaluation.<n>Despite relying on only a small number of offline snapshot loading paths for basis construction, the method accurately interpolates and extrapolates both microscopic stress fields and homogenized stresses.
• Score: 2.8396471469421027
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physics-informed operator learning is an attractive candidate for surrogate modeling of microstructures, especially in multiscale finite-element simulations. Its practical use, however, is often limited by the high cost of loss evaluation. We address this bottleneck by combining the Equilibrium Neural Operator (EquiNO) with the QR-based discrete empirical interpolation method (Q-DEIM). EquiNO learns only the modal coefficients of reduced displacement-fluctuation and first Piola-Kirchhoff stress representations built from periodic and divergence-free bases, thereby enforcing periodicity and mechanical equilibrium by construction. Q-DEIM then identifies a small set of spatial points through a column-pivoted QR factorization of the stress basis and restricts constitutive evaluations during training to these points alone. This makes full-batch second-order optimization practical for three-dimensional representative volume elements (RVEs). Homogenized first Piola-Kirchhoff stresses are recovered directly from the offline-averaged reduced stress modes, without the need to reconstruct the full stress field at inference time. We validate the framework on two three-dimensional finite-strain hyperelastic RVEs. Q-DEIM reduces the per-step training cost by roughly three orders of magnitude relative to full-field loss evaluation, while reduced homogenization achieves speed-up factors of order $10^3$ to $10^4$ over direct full-field computations. Despite relying on only a small number of offline snapshot loading paths for basis construction, the method accurately interpolates and extrapolates both microscopic stress fields and homogenized stresses, with prediction quality improving systematically as more snapshots are added.

Related papers

• Learning Orthogonal Multi-Index Models Beyond Small Initialization: Incremental Learning, Competitive Dynamics and Symmetry [52.75288960194919]
  Recent work has identified incremental learning in shallow networks trained on single-index and multi-index models.<n>We introduce a symmetry-based finite-width approximation via symmetrized networks, rather than comparing directly with an infinite-width limit.
  arXiv  Detail & Related papers  (2026-09-09T22:35:31Z)
• Scalable Lindblad Noise Learning via Stochastic Tensor-Network Simulation [48.887627688666974]
  Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies.<n>Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a simulation method, the Jump Method (TJM)<n>We demonstrate the approach on two noise models in the Ising model, in which independent dissipation rates are learned for each site up to $N_mathrmsite=16$.<n>This combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices.
  arXiv  Detail & Related papers  (2026-08-25T15:07:11Z)
• Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification [47.720075875232226]
  We introduce PCA--RaNN, a neural operator that combines a PCA-based dimensionality reduction with fixed random features.<n>It recasts operator learning as fixed regression, reducing latent regression to three orders of magnitude.
  arXiv  Detail & Related papers  (2026-06-28T15:02:26Z)
• Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks [0.6978367196609415]
  We propose a coupled LSTMGNN framework that links the temporal and spatial aspects of local stress field reconstruction.<n>We introduce a relative weighting strategy with linear warm-up to balance the data-driven reconstruction loss and a discrete divergence-based equilibrium penalty.<n>The model achieves three orders of magnitude speedup over finite element simulations and generalizes to loading sequences twice the training length, with 1.9% cumulative error.
  arXiv  Detail & Related papers  (2026-06-09T14:20:39Z)
• Shattering the Symmetry Trap in Fixed-Ansatz VQE: An Accelerated ADAPT-VQE Study of Three Pillar Molecules under Bravyi-Kitaev Mapping [0.0]
  We show how ADAPT-VQE framework shatters structural limitations across three distinct electronic and geometric molecular pillars.<n>Our numerical results show that the accelerated ADAPT-VQE framework achieves instant, exact Full Configuration Interaction.<n>This study establishes a robust, hardware-efficient path for simulating strongly correlated, highly polarized triatomic chemical environments.
  arXiv  Detail & Related papers  (2026-06-04T10:13:23Z)
• Neural Control: Adjoint Learning Through Equilibrium Constraints [7.41073008855977]
  We propose a boundary-control framework that computes trajectory-dependent, memory-efficient proxy gradients.<n>We show improved performance over gradient-free baselines such as SPSA and CEM.
  arXiv  Detail & Related papers  (2026-05-05T02:19:37Z)
• Mixture of Experts Framework in Machine Learning Interatomic Potentials for Atomistic Simulations [0.3024996106292169]
  First-principles atomistic simulations are essential for understanding complex material phenomena but are fundamentally limited by their computational cost.<n>We introduce a multifidelity "Mixture-of-Experts" framework based on the E(3)-equivariant Allegro architecture.
  arXiv  Detail & Related papers  (2026-04-28T22:04:05Z)
• Anisotropic Permeability Tensor Prediction from Porous Media Microstructure via Physics-Informed Progressive Transfer Learning with Hybrid CNN-Transformer [0.0]
  Prediction of permeability tensors from pore-scale microstructure images is essential for subsurface flow modeling, yet direct numerical simulation requires hours per sample.<n>A physics-informed deep learning framework is presented that resolves this bottleneck by combining a MaxViT hybrid CNN-Transformer architecture with progressive transfer learning and differentiable physical constraints.
  arXiv  Detail & Related papers  (2026-03-18T09:41:01Z)
• A Replicate-and-Quantize Strategy for Plug-and-Play Load Balancing of Sparse Mixture-of-Experts LLMs [64.8510381475827]
  Sparse Mixture-of-Experts (SMoE) architectures are increasingly used to scale large language models efficiently.<n>SMoE models often suffer from severe load imbalance across experts, where a small subset of experts receives most tokens while others are underutilized.<n>We present a systematic analysis of expert routing during inference and identify three findings: (i) load imbalance persists and worsens with larger batch sizes, (ii) selection frequency does not reliably reflect expert importance, and (iii) overall expert workload and importance can be estimated using a small calibration set.
  arXiv  Detail & Related papers  (2026-02-23T15:11:16Z)
• Equivariant Evidential Deep Learning for Interatomic Potentials [55.6997213490859]
  Uncertainty quantification is critical for assessing the reliability of machine learning interatomic potentials in molecular dynamics simulations.<n>Existing UQ approaches for MLIPs are often limited by high computational cost or suboptimal performance.<n>We propose textitEquivariant Evidential Deep Learning for Interatomic Potentials ($texte2$IP), a backbone-agnostic framework that models atomic forces and their uncertainty jointly.
  arXiv  Detail & Related papers  (2026-02-11T02:00:25Z)
• Optimal Sample Complexity for Single Time-Scale Actor-Critic with Momentum [62.691095807959215]
  We establish an optimal sample complexity of $O(-2)$ for obtaining an $$-optimal global policy using a single-timescale actor-critic (AC) algorithm.<n>These mechanisms are compatible with existing deep learning architectures and require only minor modifications, without compromising practical applicability.
  arXiv  Detail & Related papers  (2026-02-02T00:35:42Z)
• MPQ-DMv2: Flexible Residual Mixed Precision Quantization for Low-Bit Diffusion Models with Temporal Distillation [74.34220141721231]
  We present MPQ-DMv2, an improved textbfMixed textbfPrecision textbfQuantization framework for extremely low-bit textbfDiffusion textbfModels.
  arXiv  Detail & Related papers  (2025-07-06T08:16:50Z)
• Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity [0.2999888908665658]
  We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale.<n>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.
  arXiv  Detail & Related papers  (2025-07-05T13:11:31Z)
• PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulations [4.7903561901859355]
  We present PhysicsCorrect, a training-free correction framework that enforces PDE consistency at each prediction step.<n>Our key innovation is an efficient caching strategy that precomputes the Jacobian and its pseudoinverse during an offline warm-up phase.<n>Across three representative PDE systems, PhysicsCorrect reduces prediction errors by up to 100x while adding negligible inference time.
  arXiv  Detail & Related papers  (2025-07-03T01:22:57Z)
• Enabling Automatic Differentiation with Mollified Graph Neural Operators [73.52999622724101]
  We propose the mollified graph neural operator ($m$GNO), the first method to leverage automatic differentiation and compute exact gradients on arbitrary geometries.<n>For a PDE example on regular grids, $m$GNO paired with autograd reduced the L2 relative data error by 20x compared to finite differences.<n>It can also solve PDEs on unstructured point clouds seamlessly, using physics losses only, at resolutions vastly lower than those needed for finite differences to be accurate enough.
  arXiv  Detail & Related papers  (2025-04-11T06:16:30Z)
• On the Dynamics Under the Unhinged Loss and Beyond [104.49565602940699]
  We introduce the unhinged loss, a concise loss function, that offers more mathematical opportunities to analyze closed-form dynamics. The unhinged loss allows for considering more practical techniques, such as time-vary learning rates and feature normalization.
  arXiv  Detail & Related papers  (2023-12-13T02:11:07Z)
• Beyond the Edge of Stability via Two-step Gradient Updates [49.03389279816152]
  Gradient Descent (GD) is a powerful workhorse of modern machine learning. GD's ability to find local minimisers is only guaranteed for losses with Lipschitz gradients. This work focuses on simple, yet representative, learning problems via analysis of two-step gradient updates.
  arXiv  Detail & Related papers  (2022-06-08T21:32:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.