Learning Finite-Dimensional Representations For Koopman Operators

Mohammad Khosravi
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:1281-1281, 2021.

Abstract

In this work, the problem of learning Koopman operator of a discrete-time autonomous system is considered. The learning problem is formulated as a constrained regularized optimization over the infinite-dimensional space of linear operators. We show that under certain but general conditions, a representer theorem holds for the learning problem. This allows reformulating the problem in a finite-dimensional space without loss of any precision. Following this, we consider various cases of regularization and constraint for the latent Koopman operator including the operator norm, the Frobenius norm, and rank. Subsequently, we derive the corresponding finite-dimensional problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-khosravi21a, title = {Learning Finite-Dimensional Representations For Koopman Operators}, author = {Khosravi, Mohammad}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {1281--1281}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/khosravi21a/khosravi21a.pdf}, url = {https://proceedings.mlr.press/v144/khosravi21a.html}, abstract = {In this work, the problem of learning Koopman operator of a discrete-time autonomous system is considered. The learning problem is formulated as a constrained regularized optimization over the infinite-dimensional space of linear operators. We show that under certain but general conditions, a representer theorem holds for the learning problem. This allows reformulating the problem in a finite-dimensional space without loss of any precision. Following this, we consider various cases of regularization and constraint for the latent Koopman operator including the operator norm, the Frobenius norm, and rank. Subsequently, we derive the corresponding finite-dimensional problem.} }
Endnote
%0 Conference Paper %T Learning Finite-Dimensional Representations For Koopman Operators %A Mohammad Khosravi %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-khosravi21a %I PMLR %P 1281--1281 %U https://proceedings.mlr.press/v144/khosravi21a.html %V 144 %X In this work, the problem of learning Koopman operator of a discrete-time autonomous system is considered. The learning problem is formulated as a constrained regularized optimization over the infinite-dimensional space of linear operators. We show that under certain but general conditions, a representer theorem holds for the learning problem. This allows reformulating the problem in a finite-dimensional space without loss of any precision. Following this, we consider various cases of regularization and constraint for the latent Koopman operator including the operator norm, the Frobenius norm, and rank. Subsequently, we derive the corresponding finite-dimensional problem.
APA
Khosravi, M.. (2021). Learning Finite-Dimensional Representations For Koopman Operators. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:1281-1281 Available from https://proceedings.mlr.press/v144/khosravi21a.html.

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