Evaluation of data driven low-rank matrix factorization for accelerated solutions of the Vlasov equation
Bhavana Jonnalagadda, Stephen Becker
TL;DR
This paper introduces a neural network-based method to speed up simulations of plasma behavior by efficiently decomposing data.
Contribution
A data-driven neural network approach for low-rank matrix factorization is proposed, offering faster computation than traditional methods.
Findings
The method achieves comparable accuracy to standard techniques for interpolation tasks.
The model generalizes to unseen data but fails to extrapolate future states effectively.
The technique is well-suited for simulations with temporal stability but not for time-evolving systems.
Abstract
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 achieves comparable reconstruction accuracy for interpolation tasks, 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…
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Taxonomy
TopicsGamma-ray bursts and supernovae · Cosmology and Gravitation Theories · Solar and Space Plasma Dynamics