Online Estimation of the Koopman Operator Using Fourier Features
Tahiya Salam, Alice Kate Li, M. Ani Hsieh
TL;DR
This paper introduces an online optimization method for jointly learning the Koopman operator and its observables using Fourier features, enabling real-time analysis of complex nonlinear dynamical systems.
Contribution
It presents a novel online learning scheme that simultaneously estimates the Koopman operator and the observables, reducing reliance on handcrafted dictionaries and full dataset evaluation.
Findings
Successfully reconstructs system evolution in complex dynamics
Enables online, real-time estimation of Koopman operators
Improves feature representation of nonlinear systems
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.
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Taxonomy
TopicsModel Reduction and Neural Networks · Gaussian Processes and Bayesian Inference · Neural Networks and Applications
MethodsHigh-Order Consensuses