Data-Driven Encoding: A New Numerical Method for Computation of the Koopman Operator

This paper presents a data-driven method for constructing Koopman linear model based on the Direct Encoding (DE) formula. The prevailing methods, Dynamic Mode Decomposition (DMD) and its extensions are least squares estimates that can be shown to biased towards data densely populated. DE formula consisting of inner products nonlinear state transition function with observable functions does not incur this estimation problem thus serves as desirable alternative DMD. However, original requires knowledge equation, which is available in many practical applications. In paper, extended method, Data-Driven (DDE) operator, calculated from taken dynamic system. An effective algorithm presented computation products, their convergence true values proven. Numerical experiments verify effectiveness DDE compared Extended demonstrate robustness distribution convergent properties DDE, guaranteeing accuracy improvements additional sample points. Furthermore, applied deep learning operator further improve prediction accuracy.