# Physics-informed neural networks for modeling rate- and temperature-dependent plasticity

arXiv: https://arxiv.org/abs/2201.08363 · HTML: https://mlsanity.com/paper/2201.08363/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 75 references that are in the map.
- First posted on arXiv 20 Jan 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks](https://mlsanity.com/paper/2008.13547/) (2020)
- [Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging](https://mlsanity.com/paper/2009.04525/) (2020)
- [A machine learning based plasticity model using proper orthogonal decomposition](https://mlsanity.com/paper/2001.03438/) (2020)
- [A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relations](https://mlsanity.com/paper/1904.04058/) (2019)
- [Frequency-compensated PINNs for Fluid-dynamic Design Problems](https://mlsanity.com/paper/2011.01456/) (2020)
- [Machine Learning-Accelerated Computational Solid Mechanics: Application to Linear Elasticity](https://mlsanity.com/paper/2112.08676/) (2021)

## Built on by (most cited first, 11 of 11)

- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [PhySRNet: Physics informed super-resolution network for application in computational solid mechanics](https://mlsanity.com/paper/2206.15457/) (2022)
- [Reduced-PINN: An Integration-Based Physics-Informed Neural Networks for Stiff ODEs](https://mlsanity.com/paper/2208.12045/) (2022)
- [Spatio-Temporal Super-Resolution of Dynamical Systems using Physics-Informed Deep-Learning](https://mlsanity.com/paper/2212.04457/) (2022)
- [Physics-aware deep learning framework for linear elasticity](https://mlsanity.com/paper/2302.09668/) (2023)
- [A machine learning-based viscoelastic-viscoplastic model for epoxy nanocomposites with moisture content](https://mlsanity.com/paper/2305.08102/) (2023)
- [GPINN: Physics-informed Neural Network with Graph Embedding](https://mlsanity.com/paper/2306.09792/) (2023)
- [Finite-PINN: A Physics-Informed Neural Network with Finite Geometric Encoding for Solid Mechanics](https://mlsanity.com/paper/2412.09453/) (2024)
- [A Deep Learning Framework for Solving Hyperbolic Partial Differential Equations: Part I](https://mlsanity.com/paper/2307.04121/) (2023)
- [Transfer learning from first-principles calculations to experiments with chemistry-informed domain transformation](https://mlsanity.com/paper/2504.02848/) (2025)

## Abstract (arXiv)

This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during training, the proposed framework uses a simple strategy with no added computational complexity for selecting scalar weights that balance the interplay between different terms in the physics-based loss function. In addition, we highlight a fundamental challenge involving the selection of appropriate model outputs so that the mechanical problem can be faithfully solved using a PINN-based approach. We demonstrate the effectiveness of this approach by studying two test problems modeling the elastic-viscoplastic deformation in solids at different strain rates and temperatures, respectively. Our results show that the proposed PINN-based approach can accurately predict the spatio-temporal evolution of deformation in elastic-viscoplastic materials.