Online Estimation of the Koopman Operator Using Fourier Features

Tahiya Salam, Alice Kate Li, M. Ani Hsieh
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:1271-1283, 2023.

Abstract

Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables, acting on states of the dynamical system. This is ad hoc and requires the full dataset for evaluation. In this paper, we offer an optimization scheme to allow joint learning of the observables and Koopman operator with online data. Our results show we are able to reconstruct the evolution and represent the global features of complex dynamical systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-salam23a, title = {Online Estimation of the Koopman Operator Using Fourier Features}, author = {Salam, Tahiya and Li, Alice Kate and Hsieh, M. Ani}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {1271--1283}, year = {2023}, editor = {Matni, Nikolai and Morari, Manfred and Pappas, George J.}, volume = {211}, series = {Proceedings of Machine Learning Research}, month = {15--16 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v211/salam23a/salam23a.pdf}, url = {https://proceedings.mlr.press/v211/salam23a.html}, abstract = {Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables, acting on states of the dynamical system. This is ad hoc and requires the full dataset for evaluation. In this paper, we offer an optimization scheme to allow joint learning of the observables and Koopman operator with online data. Our results show we are able to reconstruct the evolution and represent the global features of complex dynamical systems.} }
Endnote
%0 Conference Paper %T Online Estimation of the Koopman Operator Using Fourier Features %A Tahiya Salam %A Alice Kate Li %A M. Ani Hsieh %B Proceedings of The 5th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2023 %E Nikolai Matni %E Manfred Morari %E George J. Pappas %F pmlr-v211-salam23a %I PMLR %P 1271--1283 %U https://proceedings.mlr.press/v211/salam23a.html %V 211 %X Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables, acting on states of the dynamical system. This is ad hoc and requires the full dataset for evaluation. In this paper, we offer an optimization scheme to allow joint learning of the observables and Koopman operator with online data. Our results show we are able to reconstruct the evolution and represent the global features of complex dynamical systems.
APA
Salam, T., Li, A.K. & Hsieh, M.A.. (2023). Online Estimation of the Koopman Operator Using Fourier Features. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:1271-1283 Available from https://proceedings.mlr.press/v211/salam23a.html.

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