Super-resolving 2D stress tensor field conserving equilibrium constraints using physics informed U-Net

TL;DR

This paper introduces PI-UNet, a physics-informed super-resolution neural network that predicts high-resolution stress tensor fields from low-resolution data while ensuring physical equilibrium constraints, enabling efficient finite element analysis.

Contribution

The paper presents a novel U-Net-based model that incorporates equilibrium constraints into super-resolution of stress fields, outperforming standard image super-resolution models like ESRGAN.

Findings

PI-UNet outperforms ESRGAN in stress tensor prediction.

The model generalizes well to complex shapes.

It produces physically consistent high-resolution stress fields.

Abstract

In a finite element analysis, using a large number of grids is important to obtain accurate results, but is a resource-consuming task. Aiming to real-time simulation and optimization, it is desired to obtain fine grid analysis results within a limited resource. This paper proposes a super-resolution method that predicts a stress tensor field in a high-resolution from low-resolution contour plots by utilizing a U-Net-based neural network which is called PI-UNet. In addition, the proposed model minimizes the residual of the equilibrium constraints so that it outputs a physically reasonable solution. The proposed network is trained with FEM results of simple shapes, and is validated with a complicated realistic shape to evaluate generalization capability. Although ESRGAN is a standard model for image super-resolution, the proposed U-Net based model outperforms ESRGAN model in the stress tensor prediction task.