SuperMeshing: A Novel Method for Boosting the Mesh Density in Numerical Computation within 2D Domain

TL;DR

This paper introduces SuperMeshingNet, a deep neural network that significantly enhances mesh density in 2D numerical simulations, improving accuracy and efficiency simultaneously, with proven effectiveness across multiple scaling factors.

Contribution

The paper presents a novel deep learning approach using residual dense blocks to boost mesh density in 2D finite element stress analysis, achieving high accuracy with reduced computational cost.

Findings

Effective 2X, 4X, 8X mesh density enhancement

Predicted stress field error only 0.54%

Maintains maximum stress prediction accuracy

Abstract

Due to the limit of mesh density, the improvement of the spatial precision of numerical computation always leads to a decrease in computing efficiency. Aiming at this inability of numerical computation, we propose a novel method for boosting the mesh density in numerical computation within the 2D domain. Based on the low mesh-density stress field in the 2D plane strain problem computed by the finite element method, this method utilizes a deep neural network named SuperMeshingNet to learn the non-linear mapping from low mesh-density to high mesh-density stress field, and realizes the improvement of numerical computation accuracy and efficiency simultaneously. We adopt residual dense blocks to our mesh-density boost model called SuperMeshingNet for extracting abundant local features and enhancing the prediction capacity of the model. Experimental results show that the SuperMeshingNet proposed in this work can effectively boost the spatial resolution of the stress field under the multiple scaling factors: 2X, 4X, 8X. Compared to the results of the finite element method, the predicted stress field error of SuperMeshingNet is only 0.54%, which is within the acceptable range of stress field estimation, and the SuperMeshingNet predicts the maximum stress value also without significant accuracy loss. We publicly share our work with full detail of implementation at https://github.com/zhenguonie/2021_SuperMeshing_2D_Plane_Strain.