Improving GNN-Based Multiple Scattering Simulation with Error-Driven Adaptive Edge Sampling

Recently, learning-based approaches allow very fast simulation of multiple scattering phenomena, i.e., the interactions between a field and several obstacles. They integrate a graph neural network (GNN) into the boundary element method framework (BEM), benefiting from the computational efficiency of the former and the reduction of the problem's dimensionality from the latter. Thus, the GNN estimates the solution of the boundary integral equation (BIE) on the discretized obstacle surface before applying the boundary integral representation to recover the full solution of the multiple scattering problem. While the scattered field depends on the dense graph of interactions, only a subset can be modeled by the GNN to keep the method tractable. In this paper, we introduce a new GNN architecture for simulating multiple scattering phenomena that leverages an error-driven Adaptive Edge Sampling mechanism for selecting the interactions to model based on intermediate predictions of the expected error per node. Extensive experiments demonstrate that our approach improves the estimation of the BIE solution.