Structure-Preserving Dynamical Low-Rank Approximations for Stochastic Vlasov--Poisson Equations
Abstract
We develop structure-preserving dynamical low-rank methods for stochastic Vlasov--Poisson equations with transport noise. We first derive continuous low-rank evolution equations that inherit the mass, momentum, and energy balance laws through fixed velocity modes. We then construct two augmented basis-update Galerkin (BUG) integrators based on Euler--Maruyama discretization of the Itô formulation and Heun-type discretization of the Stratonovich formulation. Both integrators combine standard basis augmentation with conservative rank truncation to preserve the selected velocity moments. We prove pathwise mass conservation and conservation of total momentum in expectation. The energy balances contain distinct stochastic corrections with identical conditional expectations and an explicitly characterized time-discretization defect. Numerical experiments illustrate the conservation properties, rank adaptation, and temporal convergence behavior of the proposed methods.
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BibTeX
@misc{cui2026structurepreserving,
title = {{Structure-Preserving Dynamical Low-Rank Approximations for Stochastic Vlasov--Poisson Equations}},
author = {Jianbo Cui and Carmela Scalone},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.00397},
eprint = {2608.00397},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00397},
}
RIS
TY - UNPB
TI - Structure-Preserving Dynamical Low-Rank Approximations for Stochastic Vlasov--Poisson Equations
AU - Jianbo Cui
AU - Carmela Scalone
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2608.00397
UR - https://arxiv.org/abs/2608.00397
AB - We develop structure-preserving dynamical low-rank methods for stochastic Vlasov--Poisson equations with transport noise. We first derive continuous low-rank evolution equations that inherit the mass, momentum, and energy balance laws through fixed velocity modes. We then construct two augmented basis-update Galerkin (BUG) integrators based on Euler--Maruyama discretization of the Itô formulation and Heun-type discretization of the Stratonovich formulation. Both integrators combine standard basis augmentation with conservative rank truncation to preserve the selected velocity moments. We prove pathwise mass conservation and conservation of total momentum in expectation. The energy balances contain distinct stochastic corrections with identical conditional expectations and an explicitly characterized time-discretization defect. Numerical experiments illustrate the conservation properties, rank adaptation, and temporal convergence behavior of the proposed methods.
ER -