Physics-constrained 3D Convolutional Neural Networks for Electrodynamics

2023/01/31 by Alexander Scheinker, Reeju Pokharel, Scheinker, Alexander +1
Computer Science · Physics and Astronomy · #Accelerator Physics (physics.acc-ph) #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Physical sciences #Gamma-ray bursts and supernovae #Machine Learning (stat.ML) #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2301.13715

openalex publication_date 2023/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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