A machine learning normalizing flow method to accelerate plasma kinetic simulations.

Particle-based kinetic simulations are time-consuming due to the multiscale dynamical processes involved and the need to follow large ensembles of particles to avoid statistical sampling errors. Here we present a novel method to overcome these computational challenges. Our approach is based on the use of Normalizing Flows, a powerful machine learning technique, to construct surrogate models for the fast integration of stochastic differential equation (SDE) corresponding to Fokker-Planck models of plasmas kinetics. In contrast to the computationally expensive Monte Carlo methods, the proposed method can directly generate samples of the SDE's final state bypassing the integration. In particular, the normalizing flow model can learn the conditional distribution of the state, i.e., the distribution of the final state conditioned to the initial state, such that the model only needs to be trained once and then used to handle arbitrary initial conditions. This feature provides significant computational savings when studying the dependence of the final state on the initial distribution. Following a discussion of the proposed method [https://arxiv.org/pdf/2306.05580.pdf] we present several applications including hot-tail generation of runaway electrons resulting from tokamak disruptions.