Improving GNN-Based Multiple Scattering Simulation with Rewiring

Rémi Marsal, Stéphanie Chaillat

Keywords: Multiple Scattering, Graph Neural Networks, Rewiring

Abstract:

The recently proposed PIBNet method introduces a learning-based framework for simulating multiple scattering phenomena.
It combines the efficiency of boundary integral representations, which transform three-dimensional problems into two-dimensional ones, with the computational advantages of graph neural networks (GNNs).
Thus, PIBNet trains a GNN to estimate the trace of the multiple scattering problem solution, i.e., the solution on the obstacle boundaries.
However, since long-range interactions are represented by edges, and only a subset can be included due to computational constraints, PIBNet GNN may fail to capture omitted interactions.
In this paper, we present a new architecture which leverages a rewiring strategy to address this issue. This increases the number of long-range interactions that are explicitly modeled in a single forward pass.
As the number of edges processed at each message passing step remains the same, the computational cost is practically not impacted.
We demonstrate improved accuracy through extensive experiments on the PIBNet benchmark.

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Submission Number: 17