We propose deep Koopman-layered models with learnable parameters in the form of Toeplitz matrices for analyzing the transition of 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 underlying the model, we can show its universality and 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 this sense, the proposed model establishes a new connection between Koopman operators and numerical linear algebraic methods.
View on arXiv@article{hashimoto2025_2410.02199,
title={ Deep Koopman-layered Model with Universal Property Based on Toeplitz Matrices },
author={ Yuka Hashimoto and Tomoharu Iwata },
journal={arXiv preprint arXiv:2410.02199},
year={ 2025 }
}