Learning reduced models for collisionless shocks

Collisionless shocks play a central role in plasma heating, magnetic field amplification and nonthermal particle acceleration in both space and astrophysical plasmas. Their study, however, has long been challenged by their multi-scale nature, where kinetic processes, operating at microscopic scales, can significantly influence the large-scale dynamics of the system. Accurately capturing the nonlinear interplay between micro- and macro-scale collisionless shock dynamics remains an outstanding problem. In this work, we explore the development of reduced models that can efficiently capture the impact of microphysical instabilities on the large-scale shock dynamics (e.g. via anomalous resistivity and viscosity). We perform first-principles particle-in-cell simulations of collisionless shocks and describe the corresponding electric field and shock potential by a generalized Ohm's law, separating the contributions of averaged (mean-field) quantities and fluctuations due to micro-instabilities. We then use neural networkd to learn how to describe the fluctuations in terms of mean fields, closing the system. We demonstrate the ability of this procedure to learn effective reduced models and to help identify the dominant microscopic processes in collisionless shocks.