Solving Electromagnetic Scattering Problems by Isogeometric Analysis with Deep Operator Learning

TL;DR

This paper introduces a hybrid method combining isogeometric analysis and deep operator networks to efficiently solve electromagnetic scattering problems, ensuring physical constraints and demonstrating strong generalization across geometries.

Contribution

The work develops a novel approach integrating neural networks with isogeometric analysis for electromagnetic problems, including physical constraints in training and showing excellent generalization.

Findings

Accurately predicts electromagnetic fields with optimal convergence rates.

Demonstrates strong generalization to unseen geometries.

Maintains physical properties like tangential continuity in predictions.

Abstract

We present a hybrid approach combining isogeometric analysis with deep operator networks to solve electromagnetic scattering problems. The neural network takes a computer-aided design representation as input and predicts the electromagnetic field in a de Rham conforming B-spline basis such that for example the tangential continuity of the electric field is respected. The physical problem is included in the loss function during training. Our numerical results demonstrate that a trained network accurately predicts the electric field, showing convergence to the analytical solution with optimal rate. Additionally, training on a variety of geometries highlights the network's generalization capabilities, achieving small error increases when applied to new geometries not included in the training set.