# Physics Informed Neural Network for Dynamic Stress Prediction

arXiv: https://arxiv.org/abs/2211.16190 · HTML: https://mlsanity.com/paper/2211.16190/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 63 references that are in the map.
- First posted on arXiv 28 Nov 2022.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021)
- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations](https://mlsanity.com/paper/1703.10230/) (2017)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios](https://mlsanity.com/paper/2205.07731/) (2022)
- [Inferring solutions of differential equations using noisy multi-fidelity data](https://mlsanity.com/paper/1607.04805/) (2016)
- [Deep Learning for Computational Chemistry](https://mlsanity.com/paper/1701.04503/) (2017)
- [Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data](https://mlsanity.com/paper/2109.12482/) (2021)
- [Deep Learning the Physics of Transport Phenomena](https://mlsanity.com/paper/1709.02432/) (2017)
- [Stress Field Prediction in Cantilevered Structures Using Convolutional Neural Networks](https://mlsanity.com/paper/1808.08914/) (2018)
- [FEA-Net: A Physics-guided Data-driven Model for Efficient Mechanical Response Prediction](https://mlsanity.com/paper/2002.01893/) (2020)
- [A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticity](https://mlsanity.com/paper/2108.07243/) (2021)

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

- [Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations](https://mlsanity.com/paper/2311.00578/) (2023)
- [Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity](https://mlsanity.com/paper/2303.13634/) (2023)
- [Mechanics-Informed Autoencoder Enables Automated Detection and Localization of Unforeseen Structural Damage](https://mlsanity.com/paper/2402.15492/) (2024)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [Generative modeling of granular flow on inclined planes using conditional flow matching](https://mlsanity.com/paper/2604.04453/) (2026)
- [Appearance-Preserving Refinement of Generated 3D Assets for Monochromatic Fabrication](https://mlsanity.com/paper/2606.26850/) (2026)

## Abstract (arXiv)

Structural failures are often caused by catastrophic events such as earthquakes and winds. As a result, it is crucial to predict dynamic stress distributions during highly disruptive events in real time. Currently available high-fidelity methods, such as Finite Element Models (FEMs), suffer from their inherent high complexity. Therefore, to reduce computational cost while maintaining accuracy, a Physics Informed Neural Network (PINN), PINN-Stress model, is proposed to predict the entire sequence of stress distribution based on Finite Element simulations using a partial differential equation (PDE) solver. 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.