# A physics-informed deep neural network for surrogate modeling in classical elasto-plasticity

arXiv: https://arxiv.org/abs/2204.12088 · HTML: https://mlsanity.com/paper/2204.12088/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 26 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Unsupervised discovery of interpretable hyperelastic constitutive laws](https://mlsanity.com/paper/2010.13496/) (2020)
- [Model-Free Data-Driven Inelasticity](https://mlsanity.com/paper/1808.10859/) (2018)
- [Data-driven fracture mechanics](https://mlsanity.com/paper/2006.03133/) (2020)
- [A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticity](https://mlsanity.com/paper/2108.07243/) (2021)
- [An accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data](https://mlsanity.com/paper/2012.00165/) (2020)

## Built on by (most cited first, 15 of 15)

- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.25781/) (2025)
- [Theory and implementation of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2311.06380/) (2023)
- [EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials](https://mlsanity.com/paper/2410.10897/) (2024)
- [Learning solution of nonlinear constitutive material models using physics-informed neural networks: COMM-PINN](https://mlsanity.com/paper/2304.06044/) (2023)
- [Efficient Surrogate Models for Materials Science Simulations: Machine Learning-based Prediction of Microstructure Properties](https://mlsanity.com/paper/2309.00305/) (2023)
- [Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2407.19326/) (2024)
- [Automatically Differentiable Model Updating (ADiMU): conventional, hybrid, and neural network material model discovery including history-dependency](https://mlsanity.com/paper/2505.07801/) (2025)
- [GRINN: A Physics-Informed Neural Network for solving hydrodynamic systems in the presence of self-gravity](https://mlsanity.com/paper/2308.08010/) (2023)
- [Physically recurrent neural network for rate and path-dependent heterogeneous materials in a finite strain framework](https://mlsanity.com/paper/2404.17583/) (2024)
- [Machine Learning Aided Modeling of Granular Materials: A Review](https://mlsanity.com/paper/2410.14767/) (2024)
- [Single- to multi-fidelity history-dependent learning with uncertainty quantification and disentanglement: application to data-driven constitutive modeling](https://mlsanity.com/paper/2507.13416/) (2025)
- [On the Limits of Tabular Hardness Metrics for Deep RL: A Study with the Pharos Benchmark](https://mlsanity.com/paper/2509.17092/) (2025)
- [Physics-Inspired Deep Learning and Transferable Models for Bridge Scour Prediction](https://mlsanity.com/paper/2407.01258/) (2024)
- [Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative](https://mlsanity.com/paper/2606.03210/) (2026)
- [On architectural choices for interpretability and thermodynamic consistency in Physically Recurrent Neural Networks in the low-data regime](https://mlsanity.com/paper/2610.04067/) (2026)

## Abstract (arXiv)

In this work, we present a deep neural network architecture that can efficiently approximate classical elasto-plastic constitutive relations. The network is enriched with crucial physics aspects of classical elasto-plasticity, including additive decomposition of strains into elastic and plastic parts, and nonlinear incremental elasticity. This leads to a Physics-Informed Neural Network (PINN) surrogate model named here as Elasto-Plastic Neural Network (EPNN). Detailed analyses show that embedding these physics into the architecture of the neural network facilitates a more efficient training of the network with less training data, while also enhancing the extrapolation capability for loading regimes outside the training data. The architecture of EPNN is model and material-independent, i.e. it can be adapted to a wide range of elasto-plastic material types, including geomaterials and metals; and experimental data can potentially be directly used in training the network. To demonstrate the robustness of the proposed architecture, we adapt its general framework to the elasto-plastic behavior of sands. We use synthetic data generated from material point simulations based on a relatively advanced dilatancy-based constitutive model for granular materials to train the neural network. The superiority of EPNN over regular neural network architectures is explored through predicting unseen strain-controlled loading paths for sands with different initial densities.