随机微分方程动态低秩逼近的进一步方法
Further Approaches of Dynamical Low-Rank Approximation for SDEs
- The University of Manchester（曼彻斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出两种新的随机微分方程动态低秩逼近方法，分别基于泛函最小化和Stratonovich公式，后者在漂移项中引入几何相关项，引发对DLRA适用性的讨论。
AI中文摘要：
在本文中，我们针对随机微分方程（SDEs）提出了两种不同于arXiv:2308.11581中所研究方法的DLRA型动力学，这两种方法分别源于泛函的最小化和（非正式地）Stratonovich公式。前一种方法类似于arXiv:1803.00499中提出的针对SDE系统的DLRA。当扩散项可微时，后一种方法在漂移项中增加了一个额外项。实际上，其推导利用Stratonovich公式将随机过程写在流形上，因此包含一个依赖于流形本身几何的项。这些进展引发了关于哪种形式更合适以及SDE的DLRA真正是什么的讨论。
英文摘要：
In this article, we propose two other DLRA-type dynamics for stochastic differential equations (SDEs) than the one studied in arXiv:2308.11581, derived from a minimization of functionals and (informally) from a Stratonovich formulation, respectively. The former approach resembles the DLRA for SDE system proposed in arXiv:1803.00499. Providing the differentiability of the diffusion, the latter procedure registers an additional term in the drift. Indeed, its derivation exploits the Stratonovich formulation to write stochastic processes on manifold, and, hence, possesses a term that depends on the geometry of the manifold itself. These developments open the debate on which formalism is more suitable and what DLRA for SDEs really is.
