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

An FEA surrogate model with Boundary Oriented Graph Embedding approach