发表机构
The Hong Kong Polytechnic University; Università dell’Aquila（香港理工大学; 拉奎拉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对含输运噪声的随机Vlasov-Poisson方程，提出保结构动态低秩方法，开发两种BUG积分器，验证其守恒特性并对比相关性能。
AI 中文摘要
针对含输运噪声的随机Vlasov-Poisson方程，我们提出保结构动态低秩方法。首先推导连续低秩演化方程，证明通过纳入与守恒量相关的固定速度模式，低秩动力学可继承原随机模型的质量、动量和能量守恒定律。随后基于两种随机离散化方案开发两种增广基更新Galerkin（BUG）积分器：一种是应用于等价Itô形式的欧拉-丸山格式，另一种是直接应用于Stratonovich形式的休恩格式，这两种选择可用于研究随机时间离散化与守恒低秩框架的相互作用。两种情况下，基增广和保守秩截断均保留相关矩空间，并在秩降低下提供鲁棒性。数值实验验证了所提方法的守恒特性，比较了两种随机形式的增广需求、随机修正项以及动量和能量行为。
英文摘要
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.
Comments30 pages
