An Attention-Guided Graph Neural Network Surrogate for Boundary Integral Computation in Physical Field Reconstruction

RongZe Gao, YuWei Wu, XinRan Ji, XingYue Ren

In practical engineering and scientific computing, a real physical system can be reduced to a boundary value problem, and the adequate boundary information to determine the interior spatial distribution and evolutionary state of the physical field can be solved with linear equations, alternatively, the the real physical problem can be treated with boundary problems with in adequate information problems in field of machine learning. This paper proposes a deep learning framework for the recovery of missing boundary information using an attention-guided graph neural network (GNN) surrogate. The framework extracts features from the physical information on the discretized boundary into a latent space, and the missing boundary quantities are then predicted by the network. Thus, the nonlinear mapping from known boundary quantities to missing boundary quantities is learned using a variational autoencoder (VAE) architecture, while an attention mechanism is incorporated to better model the correlations among different types of boundary information. Furthermore, the interior physical field can be reconstructed using the conventional boundary element method (BEM) integral formulation. The…