# Tensor-based computation of metastable and coherent sets

arXiv: https://arxiv.org/abs/1908.04741 · HTML: https://mlsanity.com/paper/1908.04741/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2019.

## Built on by (most cited first, 4 of 4)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Dynamical systems and complex networks: A Koopman operator perspective](https://mlsanity.com/paper/2405.08940/) (2024)
- [Extraction of nonlinearity in neural networks with Koopman operator](https://mlsanity.com/paper/2402.11740/) (2024)
- [Tensor-based computation of the Koopman generator via operator logarithm](https://mlsanity.com/paper/2604.07685/) (2026)

## Abstract (arXiv)

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.