Tensor network approaches for plasma dynamics
Abstract
The dynamics of plasmas are governed by a set of non-linear differential equations which remain challenging to solve directly for large 2D and 3D problems. Here we investigate how tensor networks could be applied to plasmas described by the Vlasov-Maxwell system of equations and investigate parameter regimes which show promise for efficient simulations. We show for low-dimensional problems that the simplest form of tensor networks known as a Matrix Product State performs sufficiently well, however in regimes with a strong permanent magnetic field or high-dimensional problems one may need to consider alternative tensor network geometries. We conclude the study of the Vlasov-Maxwell system with the application of tensor networks to an industrially relevant test case and validate our results against state of the art plasma solvers based on Particle-In-Cell codes. We also extend the application of tensor networks to the alternative plasma description of Magnetohydrodynamics and outline how this can be encoded using Matrix Product States.
Cite
@article{arxiv.2512.15924,
title = {Tensor network approaches for plasma dynamics},
author = {Ryan J. J. Connor and Preetma Soin and Callum W. Duncan and Andrew J. Daley},
journal= {arXiv preprint arXiv:2512.15924},
year = {2025}
}