Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval
Numerical Analysis
2020-02-17 v2 Numerical Analysis
Analysis of PDEs
Abstract
An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at each time instant by a linear combination of products of deterministic and stochastic basis functions, both of which evolve over time. A key to our proof is to find a suitable equivalent formulation of the original problem. The so-called Dual Dynamically Orthogonal formulation turns out to be convenient. Based on this formulation, the DLR approximation is recast to an abstract Cauchy problem in a suitable linear space, for which existence and uniqueness of the solution in the maximal interval are established.
Cite
@article{arxiv.2002.02356,
title = {Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval},
author = {Yoshihito Kazashi and Fabio Nobile},
journal= {arXiv preprint arXiv:2002.02356},
year = {2020}
}