# An introduction to programming Physics-Informed Neural Network-based computational solid mechanics

arXiv: https://arxiv.org/abs/2210.09060 · HTML: https://mlsanity.com/paper/2210.09060/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2022.

## Built on by (most cited first, 6 of 6)

- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Energy-based physics-informed neural network for frictionless contact problems under large deformation](https://mlsanity.com/paper/2411.03671/) (2024)
- [Utilising physics-guided deep learning to overcome data scarcity](https://mlsanity.com/paper/2211.15664/) (2022)
- [GPINN: Physics-informed Neural Network with Graph Embedding](https://mlsanity.com/paper/2306.09792/) (2023)
- [Exploring energy minimization to model strain localization as a strong discontinuity using Physics Informed Neural Networks](https://mlsanity.com/paper/2409.13241/) (2024)

## Abstract (arXiv)

Physics-informed neural network (PINN) has recently gained increasing interest in computational mechanics. In this work, we present a detailed introduction to programming PINN-based computational solid mechanics. Besides, two prevailingly used physics-informed loss functions for PINN-based computational solid mechanics are summarised. Moreover, numerical examples ranging from 1D to 3D solid problems are presented to show the performance of PINN-based computational solid mechanics. The programs are built via Python coding language and TensorFlow library with step-by-step explanations. It is worth highlighting that PINN-based computational mechanics is easy to implement and can be extended for more challenging applications. This work aims to help the researchers who are interested in the PINN-based solid mechanics solver to have a clear insight into this emerging area. The programs for all the numerical examples presented in this work are available on https://github.com/JinshuaiBai/PINN_Comp_Mech.