FieldTNN-based machine learning method for Maxwell eigenvalue problems

TL;DR

This paper introduces a novel FieldTNN-based machine learning approach for solving Maxwell eigenvalue problems in 2D and 3D, effectively handling non-tensor domains and ensuring divergence-free solutions.

Contribution

It extends TNN methods to Maxwell problems, addresses non-tensor domains, and incorporates divergence-free constraints for improved accuracy.

Findings

Demonstrates high accuracy in numerical examples

Efficiently handles 2D and 3D Maxwell problems

Filters spurious eigenpairs automatically

Abstract

The aim of this paper is to introduce a FieldTNN-based machine learning method for solving the Maxwell eigenvalue problem in both 2D and 3D domains, including both tensor and non-tensor computational regions. First, we extend the existing TNN-based approach to address the Maxwell eigenvalue problem, a fundamental challenge in electromagnetic field theory. Second, we tackle non-tensor computational domains, which represents a novel and significant contribution of this work. Third, we incorporate the divergence-free condition into the optimization process, allowing for the automatic filtering of spurious eigenpairs. Numerical examples are presented to demonstrate the efficiency and accuracy of our algorithm, underscoring its potential for broader applications in computational electromagnetics.