Embedding physical symmetries into machine-learned reduced plasma physics models via data augmentation

TL;DR

This paper demonstrates that embedding physical symmetries into machine learning models via data augmentation enhances the accuracy, efficiency, and physical consistency of reduced plasma physics models derived from kinetic simulations.

Contribution

The authors introduce a symmetry-embedding data augmentation method that improves machine learning models for plasma physics by incorporating fundamental symmetries like Lorentz and Galilean invariance.

Findings

Models trained on symmetry-augmented data better infer plasma fluid equations.

Symmetry-based augmentation suppresses spurious correlations.

Approach outperforms traditional models and closure methods.

Abstract

Machine learning is offering powerful new tools for the development and discovery of reduced models of nonlinear, multiscale plasma dynamics from the data of first-principles kinetic simulations. However, ensuring the physical consistency of such models requires embedding fundamental symmetries of plasma dynamics. In this work, we explore a symmetry-embedding strategy based on data augmentation, where symmetry-preserving transformations (e.g., Lorentz and Galilean boosts) are applied to simulation data. Using both sparse regression and neural networks, we show that models trained on symmetry-augmented data more accurately infer the plasma fluid equations and pressure tensor closures from fully kinetic particle-in-cell simulations of magnetic reconnection. We show that this approach suppresses spurious inertial-frame-dependent correlations between dynamical variables, improves data efficiency, and significantly outperforms models trained without symmetry-augmented data, as well as commonly used theoretical pressure closure models. Our results establish symmetry-based data augmentation as a broadly applicable method for incorporating physical structure into machine-learned reduced plasma models.