Tensor-based computation of metastable and coherent sets

PHYSICA D-NONLINEAR PHENOMENA

卷:427

Article

Nueske, Feliks^1,2,3  Gelss, Patrick⁴  Klus, Stefan⁵  Clementi, Cecilia^1,2,6 

[1] Rice Univ, Ctr Theoret Biol Phys, Houston, TX 77005 USA

[2] Rice Univ, Dept Chem, Houston, TX 77005 USA

[3] Paderborn Univ, Inst Math, D-33100 Paderborn, Germany

[4] Free Univ Berlin, Dept Math & Comp Sci, D-14195 Berlin, Germany

[5] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey, England

[6] Free Univ Berlin, Dept Phys, D-14195 Berlin, Germany

关键词: Koopman operator;    Extended dynamic mode decomposition;    Tensor networks;    Tensor-train format;    Dynamical systems;    Molecular dynamics;   

DOI  :  10.1016/j.physd.2021.133018

来源: Elsevier

【 摘 要 】

Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations - in particular the tensor train (TT) format - have become a valuable tool for the solution of large-scale problems in a number of fields. In this work, we combine Koopman-based models and the TT format, enabling their application to high-dimensional problems in conjunction with a rich set of basis functions or features. We derive efficient algorithms to obtain a reduced matrix representation of the system's evolution operator starting from an appropriate low-rank representation of the data. These algorithms can be applied to both stationary and non-stationary systems. We establish the infinite-data limit of these matrix representations, and demonstrate our methods' capabilities using several benchmark data sets. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free