Online Estimation of the Koopman Operator Using Fourier Features
This addresses the need for more efficient and less ad hoc methods in dynamical systems analysis, though it appears incremental as it builds on existing transfer operator frameworks.
The paper tackles the problem of learning the Koopman operator for nonlinear dynamical systems by proposing an optimization scheme that jointly learns observables and the operator using online data, enabling reconstruction of system evolution and representation of global features.
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.