Online Acceleration of Kinetic Plasma Physics Simulations Using Dynamic Mode Decomposition

Abstract

Kinetic plasma physics simulations are essential for advancing semiconductor manufacturing, but reaching quasi-steady state convergence can require millions to hundreds of millions of time steps, taking days to weeks on modern supercomputers. This thesis investigates whether Dynamic Mode Decomposition (DMD), a lightweight data-driven technique, can accelerate these simulations by learning patterns from early simulation data and using them to leap the solution forward in time. We evaluate DMD on a series of test problems of increasing complexity: a linear advection-diffusion equation, a linear diffusion equation with boundary conditions and source terms, and finally production-scale capacitively coupled plasma (CCP) simulation data from both Particle-in-Cell (PIC) and Vlasov solvers. On clean data, DMD achieves near-zero prediction error over rollout horizons at least as long as the training window, while noisy data degrades performance significantly. We tackle the noisy data challenge through temporal smoothing, data decimation, and the Hankel time-delay embedding which mitigates its effects in varying degrees. Hankel DMD shows promise for electron density in the PIC simulations, maintaining stable errors of 1–2% with no upward drift under certain hyperparameters. Most importantly, we integrate DMD directly into a running Vlasov simulation using an online simulate-learn-leap framework, achieving a 1.95x speedup to reach 1% error relative to the ground-truth steady state, with the entire DMD training and inference step completing in under one second. These results provide a proof of concept that lightweight, online data-driven methods can meaningfully reduce the cost of expensive kinetic plasma simulations without sacrificing final accuracy, offering a path toward making these simulations practical for industrial use.