Tensor approximation of the self-diffusion matrix of tagged particle processes

• Published in: Journal of computational physics 2023-05, Vol.480, p.112017, Article 112017
• Main Authors: Dabaghi, Jad, Ehrlacher, Virginie, Strössner, Christoph
• Format: Article
• Language: English
• Subjects: Alternating least squares; High-dimensional optimization; Low-rank approximations; Monte Carlo methods; Self-diffusion; Tagged particle process
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2023.112017

The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of deviations of some stochastic processes, and are thus subject to statistical noise, we propose here a tensor method in order to compute an approximation of the solution of a high-dimensional quadratic optimization problem, which enables to obtain a numerical approximation of the self-diffusion matrix. The tensor method we use here relies on an iterative scheme which builds low-rank approximations of the quantity of interest and on a carefully tuned variance reduction method so as to evaluate the various terms arising in the functional to minimize. In particular, we numerically observe here that it is much less subject to statistical noise than classical approaches. •Novel approach for computing self-diffusion matrices of tagged particle processes.•Solution of a high-dimensional minimization problem using low-rank techniques.•Less statistical noise in the approximation compared to classical approaches.