Deep Koopman-layered Model with Universal Property Based on Toeplitz Matrices

18 Sept 2024 (modified: 05 Feb 2025)Submitted to ICLR 2025EveryoneRevisionsBibTeXCC BY 4.0
Keywords: Koopman operator, Toeplitz matrix, nonautonomous dynamical system
TL;DR: We propose deep Koopman-layered models for analyzing the dynamics of time-series data, which have both theoretical solidness and flexibility.
Abstract: We propose deep Koopman-layered models with learnable parameters in the form of Toeplitz matrices for analyzing the dynamics of time-series data. The proposed model has both theoretical solidness and flexibility. By virtue of the universal property of Toeplitz matrices and the reproducing property underlined in the model, we can show its universality and the generalization property. In addition, the flexibility of the proposed model enables the model to fit time-series data coming from nonautonomous dynamical systems. When training the model, we apply Krylov subspace methods for efficient computations. In addition, the proposed model can be regarded as a neural ODE-based model. In this sense, the proposed model establishes a new connection among Koopman operators, neural ODEs, and numerical linear algebraic methods.
Supplementary Material: zip
Primary Area: learning theory
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 1504
Loading

OpenReview is a long-term project to advance science through improved peer review with legal nonprofit status. We gratefully acknowledge the support of the OpenReview Sponsors. © 2025 OpenReview