Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity

• URL: http://arxiv.org/abs/2507.05291v1
• Date: Sat, 05 Jul 2025 13:11:31 GMT
• Title: Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity
• Authors: Manuel Ricardo Guevara Garban, Yves Chemisky, Étienne Prulière, Michaël Clément,
• Abstract summary: 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.
• Score: 0.2999888908665658
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Spatiotemporal Field Generation Based on Hybrid Mamba-Transformer with Physics-informed Fine-tuning [46.67399627400437]
  This research confronts the challenge of substantial physical equation discrepancies in the generation of physical fields through trained models.<n>A physical field generation model, named HMT-PF, is developed based on the hybrid Mamba-Transformer architecture.
  arXiv  Detail & Related papers  (2025-05-16T14:40:56Z)
• Global Stress Generation and Spatiotemporal Super-Resolution Physics-Informed Operator under Dynamic Loading for Two-Phase Random Materials [4.696265806758292]
  Under dynamic loading, material failure in random materials is often associated with stress concentration.<n>In this study, we propose a framework for global stress generation and supertemporal superresolution in TRMs under dynamic loading.<n>The influence of data-driven and physics-informed loss function weights on model accuracy is explored in detail.
  arXiv  Detail & Related papers  (2025-04-26T08:37:29Z)
• GausSim: Foreseeing Reality by Gaussian Simulator for Elastic Objects [55.02281855589641]
  GausSim is a novel neural network-based simulator designed to capture the dynamic behaviors of real-world elastic objects represented through Gaussian kernels.<n>We leverage continuum mechanics and treat each kernel as a Center of Mass System (CMS) that represents continuous piece of matter.<n>In addition, GausSim incorporates explicit physics constraints, such as mass and momentum conservation, ensuring interpretable results and robust, physically plausible simulations.
  arXiv  Detail & Related papers  (2024-12-23T18:58:17Z)
• Event-Based Simulation of Stochastic Memristive Devices for Neuromorphic Computing [41.66366715982197]
  We build a general model of memristors suitable for the simulation of event-based systems. We extend an existing general model of memristors to an event-driven setting. We demonstrate an approach for fitting the parameters of the event-based model to the drift model.
  arXiv  Detail & Related papers  (2024-06-14T13:17:19Z)
• Enforcing the Principle of Locality for Physical Simulations with Neural Operators [0.0]
  Time-dependent partial differential equations (PDEs) are strictly local-dependent according to the principle of locality in physics.<n>Deep learning architecture cannot strictly enforce the local-dependency as it inevitably increases the scope of information to make local predictions.<n>This paper proposes a data decomposition method to strictly limit the scope of information for neural operators making local predictions.
  arXiv  Detail & Related papers  (2024-05-02T14:24:56Z)
• Neural Stress Fields for Reduced-order Elastoplasticity and Fracture [43.538728312264524]
  We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. Key innovation is training a low-dimensional manifold for the Kirchhoff stress field via an implicit neural representation. We demonstrate dimension reduction by up to 100,000X and time savings by up to 10X.
  arXiv  Detail & Related papers  (2023-10-26T21:37:32Z)
• NeuralClothSim: Neural Deformation Fields Meet the Thin Shell Theory [70.10550467873499]
  We propose NeuralClothSim, a new quasistatic cloth simulator using thin shells. Our memory-efficient solver operates on a new continuous coordinate-based surface representation called neural deformation fields.
  arXiv  Detail & Related papers  (2023-08-24T17:59:54Z)
• Neuro-DynaStress: Predicting Dynamic Stress Distributions in Structural Components [10.588266927411434]
  It is crucial to predict dynamic stress distributions during highly disruptive events in real-time. Deep learning model, Neuro-DynaStress, is proposed to predict the entire sequence of stress distribution based on finite element simulations.
  arXiv  Detail & Related papers  (2022-12-19T03:02:26Z)
• Physics Informed Neural Network for Dynamic Stress Prediction [10.588266927411434]
  A Physics Informed Neural Network (PINN) model is proposed to predict the entire sequence of stress distribution based on Finite Element simulations. Using automatic differentiation, we embed a PDE into a deep neural network's loss function to incorporate information from measurements and PDEs. The PINN-Stress model can predict the sequence of stress distribution in almost real-time and can generalize better than the model without PINN.
  arXiv  Detail & Related papers  (2022-11-28T16:03:21Z)
• Robust Learning of Physics Informed Neural Networks [2.86989372262348]
  Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE.
  arXiv  Detail & Related papers  (2021-10-26T00:10:57Z)
• Physics informed neural networks for continuum micromechanics [68.8204255655161]
  Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization. It is shown, that the domain decomposition approach is able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $mu$CT-scans.
  arXiv  Detail & Related papers  (2021-10-14T14:05:19Z)
• GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles [60.12186997181117]
  Prediction of a molecule's 3D conformer ensemble from the molecular graph holds a key role in areas of cheminformatics and drug discovery. Existing generative models have several drawbacks including lack of modeling important molecular geometry elements. We propose GeoMol, an end-to-end, non-autoregressive and SE(3)-invariant machine learning approach to generate 3D conformers.
  arXiv  Detail & Related papers  (2021-06-08T14:17:59Z)

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.