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

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-differentiable 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.

💡 Research Summary

This paper presents a novel data‑driven framework for learning plasma collision operators directly from phase‑space diagnostics, leveraging differentiable kinetic simulators coupled with Particle‑in‑Cell (PIC) data. Traditional collision modeling in plasmas relies on analytically derived operators such as the Fokker‑Planck (FP) operator, which assumes small‑angle scattering and weak coupling. However, in strongly coupled, magnetized, or relativistic regimes these assumptions break down, and first‑principles simulations (e.g., Molecular Dynamics, PIC) become essential. Extracting accurate operators from such simulations has remained a challenge.

The authors extend their previous work (which learned time‑invariant FP operators) in two key directions: (1) they introduce a time‑dependent FP operator that captures evolving background distributions, and (2) they formulate a more general integro‑differential operator, C