A deep learning framework for solution and discovery in solid mechanics

TL;DR

This paper introduces a physics-informed deep learning framework using PINNs for solving and discovering solutions in solid mechanics, demonstrating improved accuracy, convergence, and robustness over traditional methods.

Contribution

It proposes a multi-network PINN model for solid mechanics, extending to nonlinear problems, and shows its advantages over FEM and transfer learning capabilities.

Findings

Multi-network PINN improves accuracy in solid mechanics problems.

PINNs outperform FEM in convergence and robustness.

Framework enables transfer learning for rapid re-training.

Abstract

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN, and explore in detail the application to linear elasticity, and illustrate its extension to nonlinear problems through an example that showcases von~Mises elastoplasticity. While common PINN algorithms are based on training one deep neural network (DNN), we propose a multi-network model that results in more accurate representation of the field variables. To validate the model, we test the framework on synthetic data generated from analytical and numerical reference solutions. We study convergence of the PINN model, and show that Isogeometric Analysis (IGA) results in superior accuracy and convergence characteristics compared with classic low-order Finite Element Method (FEM). We also show the applicability of the framework for transfer learning, and find vastly accelerated convergence during network re-training. Finally, we find that honoring the physics leads to improved robustness: when trained only on a few parameters, we find that the PINN model can accurately predict the solution for a wide range of parameters new to the network---thus pointing to an important application of this framework to sensitivity analysis and surrogate modeling.