  This paper proposes a data-driven framework to learn a finite-dimensional
approximation of a Koopman operator for approximating the state evolution of a
dynamical system under noisy observations. To this end, our proposed solution
has two main advantages. First, the proposed method only requires the
measurement noise to be bounded. Second, the proposed method modifies the
existing deep Koopman operator formulations by characterizing the effect of the
measurement noise on the Koopman operator learning and then mitigating it by
updating the tunable parameter of the observable functions of the Koopman
operator, making it easy to implement. The performance of the proposed method
is demonstrated on several standard benchmarks. We further compare the
presented method with similar methods proposed in the latest literature on
Koopman learning.
