DeepAI AI Chat
Log In Sign Up

Tensor-based EDMD for the Koopman analysis of high-dimensional systems

by   Feliks Nüske, et al.

Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory -- with extended dynamic mode decomposition (EDMD) being a cornerstone of the field. 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 EDMD and the TT format, enabling the application of EDMD to high-dimensional problems in conjunction with a large set of features. We present the construction of different TT representations of tensor-structured data arrays. Furthermore, we also derive efficient algorithms to solve the EDMD eigenvalue problem based on those representations and to project the data into a low-dimensional representation defined by the eigenvectors. We prove that there is a physical interpretation of the procedure and demonstrate its capabilities by applying the method to benchmark data sets of molecular dynamics simulation.


page 1

page 20


Alternating linear scheme in a Bayesian framework for low-rank tensor approximation

Multiway data often naturally occurs in a tensorial format which can be ...

A robust GMRES algorithm in Tensor Train format

We consider the solution of linear systems with tensor product structure...

High-Dimensional Low-Rank Tensor Autoregressive Time Series Modeling

Modern technological advances have enabled an unprecedented amount of st...

Solving high-dimensional nonlinear filtering problems using a tensor train decomposition method

In this paper, we propose an efficient numerical method to solve high-di...

A New Approach to Multilinear Dynamical Systems and Control

The current paper presents a new approach to multilinear dynamical syste...

Post-Processing of High-Dimensional Data

Scientific computations or measurements may result in huge volumes of da...