Solving Electromagnetic Scattering Problems by Isogeometric Analysis with Deep Operator Learning

TL;DR

A hybrid approach combining isogeometric analysis with deep operator networks to solve electromagnetic scattering problems by taking a computer aided design representation as input and predicts the electromagnetic field in a de Rham conforming B-spline basis.

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.

Figures (2)

• Figure 1: Maximum pointwise error of the electric field on the unit sphere with wave number $\kappa = 2$. The stopping criterion was $\epsilon \leq 10^{-9}$.
• Figure 2: Visualization of the predicted surface current density for an unseen geometry excited by a dipole positioned inside. The stopping criterion was $\epsilon \leq 2\cdot10^{-8}$.