Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization method using artificial neural networks, specifically with convolutional layer architecture, that trains on existing simulation data. At inference time, the model outputs a low-rank decomposition of the distribution field of the charged particles, and we demonstrate that this step is faster than the standard linear algebra technique. Numerical experiments show that the method effectively interpolates time-series data, generalizing to unseen test data in a manner beyond just memorizing training data; patterns in factorization also inherently followed the same numerical trend as those within algebraic methods (e.g., truncated singular-value decomposition). However, when training on the first 70% of a time-series data and testing on the remaining 30%, the method fails to meaningfully extrapolate. Despite this limiting result, the technique may have benefits for simulations in a statistical steady-state or otherwise showing temporal stability.
Accelerated Parallel and Distributed Algorithm using Limited Internal Memory for Nonnegative Matrix Factorization
Japan Advanced Institute of Science and Technology（日本科学技术高等学院）；University of Engineering and Technology, Vietnam National University, Hanoi（越南国立大学河内大学工程技术学院）；John von Neumann Institute, Vietnam National University, Ho Chi Minh City（越南国立大学胡志明市冯·诺依曼研究所）
