Learning collision operators from plasma phase space data using differentiable simulators

We propose a methodology to infer collision operators from phase space data of plasma dynamics. Our approach combines a differentiable kinetic simulator, whose core component in this work is a differentiable Fokker-Planck solver, with a gradient-based optimisation method to learn the collisional operators that best describe the phase space dynamics. We test our method using data from two-dimensional Particle-in-Cell simulations of spatially uniform thermal plasmas, and learn the collision operator that captures the self-consistent electromagnetic interaction between finite-size charged particles over a wide variety of simulation parameters. We demonstrate that the learned operators are more accurate than alternative estimates based on particle tracks, while making no prior assumptions about the relevant time-scales of the processes and significantly reducing memory requirements. We find that the retrieved operators, obtained in the non-relativistic regime, are in excellent agreement with theoretical predictions derived for electrostatic scenarios. Our results show that differentiable simulators offer a powerful and computational efficient approach to infer novel operators for a wide rage of problems, such as electromagnetically dominated collisional dynamics and stochastic wave-particle interactions.