A pseudo-reversible normalizing flow method for plasma kinetic simulations

Particle-based kinetic computations in magnetically confined plasmas require the numerical integration of stochastic differential equations (SDE) in which the determinist part describes the Hamiltonian orbit dynamics (e.g., full-orbit, guiding center, or gyro-average) and the stochastic part collisions (for neoclassical transport) and diffusion (for anomalous transport due to turbulence and/or magnetic stochasticity). A potential limitation of this Monte-Carlo approach is that, to avoid statistical sampling errors, the SDE need to be solved for very large ensembles of particles. To overcome this limitation, we recently proposed a pseudo-reversible normalizing flow (PR-NF) machine-learning method for the acceleration of the integration of SDE [https://arxiv.org/pdf/2306.05580.pdf]. After training, the PR-NF model can directly generate samples of the SDE’s final state without simulating trajectories. Going beyond previous applications to 2D phase-space models of hot-tail generation of runaway electron (RE), here we consider higher dimensional RE kinetic models with collision operators including large-angle collisions (avalanche source).