aiqbench analysis
This research advances data-driven modeling of nonlinear dynamical systems by combining Koopman operator theory with low-rank tensor train formats to mitigate the curse of dimensionality. By leveraging operator logarithms, the method enables accurate system identification from sparse data without requiring time differentiation, offering a scalable solution for high-dimensional physics-informed machine learning tasks.
Tensor-based computation of the Koopman generator via operator logarithm
arXiv:2604.07685v2 Announce Type: replace Abstract: Identifying governing equations of nonlinear dynamical systems from data is challenging. While sparse identification of nonlinear dynamics (SINDy) and its extensions are widely used for system identification, operator-logarithm approaches use the logarithm to avoid time differentiation, enabling larger sampling intervals. However, they still suffer from the curse of dimensionality. Then, we propose a data-driven method to compute the Koopman generator in a low-rank tensor train (TT) format by taking logarithms of Koopman eigenvalues while preserving the TT format. Experiments on 4-dimensional Lotka-Volterra and 10-dimensional Lorenz-96 systems show accurate recovery of vector field coefficients and scalability to higher-dimensional systems.
Abstract:Identifying governing equations of nonlinear dynamical systems from data is challenging. While sparse identification of nonlinear dynamics (SINDy) and its extensions are widely used for system identification, operator-logarithm approaches use the logarithm to avoid time differentiation, enabling larger sampling intervals. However, they still suffer from the curse of dimensionality. Then, we propose a data-driven method to compute the Koopman generator in a low-rank tensor train (TT) format by taking logarithms of Koopman eigenvalues while preserving the TT format. Experiments on 4-dimensional Lotka-Volterra and 10-dimensional Lorenz-96 systems show accurate recovery of vector field coefficients and scalability to higher-dimensional systems.
Machine Learning (cs.LG)
arXiv:2604.07685 [cs.LG]
(or arXiv:2604.07685v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2604.07685 Focus to learn more arXiv-issued DOI via DataCite
Nonlinear Theory and its Applications, IEICE 17, pp. 1406-1417 (2026)
https://doi.org/10.1587/nolta.2026NCP0003 Focus to learn more DOI(s) linking to related resources
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 210 words
