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Title: A Data Driven, Convex Optimization Approach to Learning Koopman Operators}
Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models. However, choosing appropriate models and bounding the approximation error is far from trivial. Motivated by these difficulties, in this paper we propose an optimization based approach to learning Koopman operators from data. Our results show that the Koopman operator, the associated Hilbert space of observables and a suitable dictionary can be obtained by solving two rank-constrained semi-definite programs (SDP). While in principle these problems are NP-hard, the use of standard relaxations of rank leads to convex SDPs.
Authors:
Award ID(s):
1814631 2038493 1646121
Publication Date:
NSF-PAR ID:
10291531
Journal Name:
Proceedings of Machine Learning Research
Volume:
144
Page Range or eLocation-ID:
436-446
ISSN:
2640-3498
Sponsoring Org:
National Science Foundation
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