An FEA surrogate model with Boundary Oriented Graph Embedding approach

TL;DR

This paper introduces the Boundary Oriented Graph Embedding (BOGE) approach, a novel GNN-based surrogate model that efficiently predicts physical fields and topological optimization results in large-scale FEA problems, especially on triangular meshes.

Contribution

The BOGE approach uniquely embeds boundary and local neighbor information into GNNs, enabling accurate and efficient regression of FEA results and topological optimization outcomes.

Findings

Achieves 2.41% MAPE in stress field prediction

Regresses topological optimization with 1.58% error in elements

Demonstrates potential for general deep-learning-based FEA simulation

Abstract

In this work, we present a Boundary Oriented Graph Embedding (BOGE) approach for the Graph Neural Network (GNN) to serve as a general surrogate model for regressing physical fields and solving boundary value problems. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed structured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based FEA results, which cannot be realized by other machine-learning-based surrogate methods. Focusing on the cantilever beam problem, our BOGE approach cannot only fit the distribution of stress fields but also regresses the topological optimization results, which show its potential of realizing abstract decision-making design process. The BOGE approach with 3-layer DeepGCN model \textcolor{blue}{achieves the regression with MSE of 0.011706 (2.41\% MAPE) for stress field prediction and 0.002735 MSE (with 1.58\% elements having error larger than 0.01) for topological optimization.} The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and design-related areas.