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

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.