Physics-constrained 3D Convolutional Neural Networks for Electrodynamics

TL;DR

This paper introduces a physics-constrained 3D convolutional neural network designed to solve Maxwell's equations, accurately modeling electromagnetic fields of relativistic charged particles while inherently satisfying physical constraints.

Contribution

It develops a novel neural network architecture that incorporates physical laws directly into the learning process for electromagnetic field prediction.

Findings

The PCNN accurately predicts electromagnetic fields from charge and current densities.

The model enforces divergence-free magnetic fields by design.

It effectively incorporates physical constraints into deep learning for electrodynamics.

Abstract

We present a physics-constrained neural network (PCNN) approach to solving Maxwell's equations for the electromagnetic fields of intense relativistic charged particle beams. We create a 3D convolutional PCNN to map time-varying current and charge densities J(r,t) and p(r,t) to vector and scalar potentials A(r,t) and V(r,t) from which we generate electromagnetic fields according to Maxwell's equations: B=curl(A), E=-div(V)-dA/dt. Our PCNNs satisfy hard constraints, such as div(B)=0, by construction. Soft constraints push A and V towards satisfying the Lorenz gauge.