A Neural Score-Based Method for Deterministic Collisional Plasma Simulation

Vasily Ilin, Jingwei Hu

Keywords: plasma simulation; collisional PIC; Vlasov–Maxwell–Landau; score models; diffusion/transport models; conservation laws

TL;DR: A faster, more accurate collisional PIC method for Vlasov–Maxwell–Landau using NN-based score estimation.

Abstract: Plasma modeling is central to the design of nuclear fusion reactors, yet simulating collisional plasma kinetics from first principles remains a formidable computational challenge: the Vlasov-Maxwell-Landau (VML) equations couple six-dimensional phase-space transport to self-consistent electromagnetic fields through the nonlinear, nonlocal Landau collision operator. The sole deterministic particle method for the full VML system estimates the velocity score function via the blob method -- a kernel-based approximation that incurs $O(n^2)$ cost, does not scale well in dimension, and has unsatisfactory performance in low-density regimes. We replace the blob score estimator with score-based transport modeling (SBTM), in which a neural network is trained on-the-fly via implicit score matching at $O(n)$ cost. We prove that the collision operator preserves mass, momentum, and kinetic energy for any score approximation, and dissipates an estimated entropy. On three canonical benchmarks -- Landau damping, two-stream instability, and Weibel instability -- SBTM is more accurate than the blob method, achieves correct long-time thermalization to Maxwellian equilibrium where the blob method fails, and delivers $50\%$ faster runtime with $4\times$ lower peak memory.

Journal Opt In: Yes, I want to participate in the IOP focus collection submission

Journal Corresponding Email: [e-mail]

Journal Notes: We will be ready to submit the final journal version of the paper by April 1.

Submission Number: 101