Neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics

Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze dynamics with a linear regime lifting observations using function. For analysis, need to find an appropriate lift Although several methods have been proposed estimating function based on neural networks, the existing train networks without analysis. In this paper, propose dynamic mode decomposition, in are trained such that forecast error is minimized when modeled decomposition lifted space. With our method, backpropagated through and enabling end-to-end learning of When information available frequencies or growth rates dynamics, method exploit it as regularizers training. We also extension approach influenced exogenous control time-series. Our experiments demonstrate effectiveness terms eigenvalue estimation performance.