[2603.25832] A Neural Score-Based Particle Method for the Vlasov-Maxwell-Landau System

Mathematics > Numerical Analysis arXiv:2603.25832 (math) [Submitted on 26 Mar 2026] Title:A Neural Score-Based Particle Method for the Vlasov-Maxwell-Landau System Authors:Vasily Ilin, Jingwei Hu View a PDF of the paper titled A Neural Score-Based Particle Method for the Vlasov-Maxwell-Landau System, by Vasily Ilin and 1 other authors View PDF HTML (experimental) 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) system describes six-dimensional phase-space transport under self-consistent electromagnetic fields together with the nonlinear, nonlocal Landau collision operator. A recent deterministic particle method for the full VML system estimates the velocity score function via the blob method, a kernel-based approximation with $O(n^2)$ cost. In this work, 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 approximated collision operator preserves momentum and kinetic energy, and dissipates an estimated entropy. We also characterize the unique global steady state of the VML system and its electrostatic reduction, providing the ground truth for numerical validation. On three canonical benchmarks -- Landau damping, two-stream instability, and Weibel instability -- SBTM is...