Physics-constrained machine learning for electrodynamics without gauge ambiguity based on Fourier transformed...

Area of Science:

• Computational Electrodynamics
• Applied Physics
• Machine Learning

Background:

• Maxwell's equations are fundamental to classical electrodynamics but can be challenging to solve numerically.
• Existing methods may face issues with gauge ambiguity and computational expense.
• Developing efficient and accurate numerical methods is crucial for simulating electromagnetic phenomena.

Purpose of the Study:

• To develop a novel physics-constrained neural network approach for solving Maxwell's equations.
• To address gauge ambiguity in electrodynamic simulations.
• To create a computationally efficient method for predicting electromagnetic fields.

Main Methods:

• Utilized a Fourier transformation-based representation of Maxwell's equations.
• Developed the Fourier-Helmholtz-Maxwell neural operator method incorporating Gauss's and Faraday's laws as hard constraints.
• Employed an encoder-decoder network (specifically a U-Net architecture) to solve for the transverse components of the Fourier transformed vector potential.

Main Results:

• The U-Net architecture demonstrated superior performance, training faster, achieving higher accuracy, and generalizing better than other examined architectures.
• The method successfully predicted electromagnetic fields generated by intense relativistic charged particle beams.
• The approach was orders of magnitude faster than conventional simulations and generalized well to unseen data.

Conclusions:

• The Fourier-Helmholtz-Maxwell neural operator method provides an efficient and accurate solution for electrodynamics problems.
• Physics-constrained neural networks can effectively solve complex electromagnetic field simulations.
• The method shows promise for real-time applications and rapid re-training for new datasets.