Data-Driven Methods for Anomalous Resistivity in 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 its multi-scale nature, where microscopic-scale kinetic processes can influence the large-scale dynamics of the system and vice-versa. Accurately capturing the nonlinear interplay between micro- and macro-scale collisionless shock dynamics remains an outstanding problem.

In this Thesis, we explore the development of data-driven reduced models that can more efficiently capture the impact of microphysical instabilities on the largescale shock dynamics. We perform first-principles particle-in-cell simulations of collisionless shocks and describe the corresponding electric field by a generalized Ohm’s law, separating the contributions of transversely-averaged (mean-field) quantities and fluctuations due to transverse micro-instabilities. We then use convolutional neural networks 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 reproduce the spatiotemporal profile of the anomalous electric field induced in a collisionless shock. We then explore network interrogation methods to help identify the physical terms most relevant to our network-based surrogate anomalous field. This led to the identification of the mean quantities that control the dynamics of collisionless shocks and, in the future, could also inform the search for more interpretable reduced models. Our work opens the way to the incorporation of data-driven reduced models on fluid codes that could capture the effect of unresolved kinetic processes on the largescale collisionless shock dynamics.