Surrogate Modeling of Dynamics From Sparse Data Using Maximum Entropy Basis Functions

Abstract

In this paper we present a data driven approach for approximating dynamical systems. A dynamics is approximated using basis functions, which are derived from maximization of the information-theoretic entropy, and can be generated directly from the data provided. This approach has advantages over other methods, where a dictionary of basis functions have to be provided by the user, which is non trivial in some applications. We compare the accuracy of the proposed data-driven modeling approach to existing methods in the literature, and demonstrate that for some applications the maximum entropy basis functions provide significantly more accurate models.