Machine Learning-Accelerated Computational Solid Mechanics: Application to Linear Elasticity

TL;DR

This paper introduces a physics-informed deep learning framework that reconstructs high-resolution deformation fields from low-resolution data in linear elasticity, matching the accuracy of high-resolution simulations without labeled data.

Contribution

It presents a novel super-resolution method leveraging physics-informed neural networks to enhance low-resolution elastic deformation fields without requiring high-resolution training data.

Findings

Super-resolved fields match high-resolution solver accuracy

Method satisfies governing physical laws

Performance comparison of two deep learning architectures

Abstract

This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage the governing equations and boundary conditions of the physical system to train the model without using any high-resolution labeled data. The proposed approach is applied to obtain the super-resolved deformation fields from the low-resolution stress and displacement fields obtained by running simulations on a coarse mesh for a body undergoing linear elastic deformation. We demonstrate that the super-resolved fields match the accuracy of an advanced numerical solver running at 400 times the coarse mesh resolution, while simultaneously satisfying the governing laws. A brief evaluation study comparing the performance of two deep learning based super-resolution architectures is also presented.