mlsanityData to 7 Oct 2026

Physics informed neural networks for continuum micromechanics

arXiv 2110.07374 ↗First posted 14 Oct 2021cs.LGcited by 46

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Abstract (arXiv)

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial differential equations. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization. In this work we consider material non-linearities invoked by material inhomogeneities with sharp phase interfaces. This constitutes a challenging problem for a method relying on a global ansatz. To overcome convergence issues, adaptive training strategies and domain decomposition are studied. 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 μCT-scans.

Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). Builds on 20 of its 55 references that are in the map. First posted on arXiv 14 Oct 2021.

Builds on

20 of 55 references.

References · 20

  1. 2015Rethinking the Inception Architecture for Computer Visioncited by 5,451
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  4. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  5. 2020Universal Differential Equations for Scientific Machine Learningcited by 345
  6. 2020Understanding and mitigating gradient pathologies in physics-informed neural networkscited by 134
  7. 2017A unified deep artificial neural network approach to partial differential equations in complex geometriescited by 122
  8. 2020Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networkscited by 122
  9. 2019An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applicationscited by 118
  10. 2021Parallel Physics-Informed Neural Networks via Domain Decompositioncited by 112
  11. 2019Physics-Informed Neural Networks for Power Systemscited by 80
  12. 2020Physics-informed deep learning for incompressible laminar flowscited by 54
8 more
  1. 2016Deep Learning in Bioinformaticscited by 48
  2. 2020Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacturecited by 48
  3. 2020Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networkscited by 42
  4. 2020Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imagingcited by 40
  5. 2020On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEscited by 31
  6. 2021On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling samplingcited by 24
  7. 2020Energy-based error bound of physics-informed neural network solutions in elasticitycited by 15
  8. 2021A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticitycited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 8; 2023: 17; 2024: 10; 2025: 7; 2026: 4.

46 papers.

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  1. 2022A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element methodcited by 33
  2. 2022MAgNET: A Graph U-Net Architecture for Mesh-Based Simulationscited by 26
  3. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  4. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  5. 2023Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Reviewcited by 15
  6. 2023Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domainscited by 14
  7. 2023Theory and implementation of inelastic Constitutive Artificial Neural Networkscited by 12
  8. 2022Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanicscited by 11
  9. 2022Spiking neural networks for nonlinear regressioncited by 10
  10. 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)cited by 9
  11. 2024Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problemcited by 8
  12. 2023Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applicationscited by 6
34 more
  1. 2024Physics-informed Discretization-independent Deep Compositional Operator Networkcited by 6
  2. 2024NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elementscited by 6
  3. 2023Deep learning for full-field ultrasonic characterizationcited by 5
  4. 2023Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performancecited by 5
  5. 2023Stochastic stiffness identification and response estimation of Timoshenko beams via physics-informed Gaussian processescited by 5
  6. 2024Neural networks for bifurcation and linear stability analysis of steady states in partial differential equationscited by 5
  7. 2022Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Datacited by 4
  8. 2023Learning from Integral Losses in Physics Informed Neural Networkscited by 4
  9. 2023Physics-guided training of GAN to improve accuracy in airfoil design synthesiscited by 4
  10. 2023Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materialscited by 3
  11. 2023Identifying Constitutive Parameters for Complex Hyperelastic Materials using Physics-Informed Neural Networkscited by 3
  12. 2023Probabilistic Physics-integrated Neural Differentiable Modeling for Isothermal Chemical Vapor Infiltration Processcited by 3
  13. 2025Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energiescited by 3
  14. 2025EquiNO: A Physics-Informed Neural Operator for Multiscale Simulationscited by 3
  15. 2025Generalized invariants meet constitutive neural networks: A novel framework for hyperelastic materialscited by 3
  16. 2024Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networkscited by 2
  17. 2025Homogenization with Guaranteed Bounds via Primal-Dual Physically Informed Neural Networkscited by 2
  18. 2022MRF-PINN: A Multi-Receptive-Field convolutional physics-informed neural network for solving partial differential equationscited by 1
  19. 2022Utilising physics-guided deep learning to overcome data scarcitycited by 1
  20. 2023Incorporating sufficient physical information into artificial neural networks: a guaranteed improvement via physics-based Rao-Blackwellizationcited by 1
  21. 2024Physics-informed DeepONet with stiffness-based loss functions for structural response predictioncited by 1
  22. 2024Finite-PINN: A Physics-Informed Neural Network with Finite Geometric Encoding for Solid Mechanicscited by 1
  23. 2025Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structurescited by 1
  24. 2025A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materialscited by 1
  25. 2026A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentialscited by 1
  26. 2023Detecting hidden structures from a static loading experiment: topology optimization meets physics-informed neural networkscited by 0
  27. 2023Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear PDEscited by 0
  28. 2023Graph Neural Networks for Dynamic Modeling of Roller Bearingcited by 0
  29. 2024Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networkscited by 0
  30. 2024Enhancing Multiscale Simulations with Constitutive Relations-Aware Deep Operator Networkscited by 0
  31. 2025Predicting Stress in Two-phase Random Materials and Super-Resolution Method for Stress Images by Embedding Physical Informationcited by 0
  32. 2026Adaptively trained Physics-informed Radial Basis Function Neural Networks for Solving Multi-asset Option Pricing Problemscited by 0
  33. 2026PiGRAND: Physics-informed Graph Neural Diffusion for Intelligent Additive Manufacturingcited by 0
  34. 2026A variational physics-informed graph neural network for heterogeneous solid mechanicscited by 0