An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

In this work, we present a Boundary Oriented Graph Embedding (BOGE) approach for the Graph Neural Network (GNN) to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured 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. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model 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 CAD design-related areas.