Description
Collisionless shocks are a quintessential problem in astrophysical plasma processes, driving plasma heating, magnetic field amplification, and particle acceleration. However, modeling these systems is notoriously difficult due to their multi-scale nature, where kinetic processes operating at microscopic scales significantly influence large-scale dynamics. Capturing the nonlinear interplay between the scales that contribute to shock dynamics remains an outstanding problem. In this work, we explore the development of data-driven spatial closures for fluid equations that encapsulate the impact of microphysical instabilities on large-scale dynamics via anomalous-resistivity-type terms. We perform first-principles particle-in-cell simulations of collisionless shocks and describe the corresponding electric field and shock potential through a generalized Ohm's law, separating the contributions of averaged (mean-field) quantities from fluctuations due to micro-instabilities. We then employ neural networks to map macroscopic mean fields to these microscopic fluctuations, thereby closing the fluid system. We demonstrate the ability of this procedure to learn effective reduced models and to identify the dominant microscopic processes governing collisionless shocks through model explainability.