Learning time-dependent and integro-differential collision operators from plasma phase space data using differentiable simulators

Abstract

Collisional and stochastic wave-particle dynamics in plasmas far from equilibrium are complex, temporally evolving, stochastic processes which are challenging to model. In this work, we extend previous methods coupling differentiable kinetic simulators and plasma phase space diagnostics to learn collision operators that account for time-varying background distributions. We also introduce a more general integro-differential operator formulation to probe relevant terms in the collision operator. To validate the proposed methodology we use data generated by self-consistent electromagnetic Particle-in-Cell simulations. We show that both approaches recover operators that can accurately reproduce the plasma phase space dynamics while being more accurate than estimates based on particle track statistics. These results further demonstrate the potential of using differentiable simulators to infer collision operators for scenarios where no closed form solution exists or deviations from existing theory are expected.