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

TL;DR

This paper introduces a data-driven method for modeling dynamical systems using maximum entropy basis functions derived directly from data, offering improved accuracy over traditional dictionary-based approaches.

Contribution

The paper proposes a novel approach to approximate dynamics with basis functions generated via maximum entropy, eliminating the need for predefined dictionaries.

Findings

Maximum entropy basis functions improve model accuracy in some applications.

The method is data-driven and does not require predefined basis dictionaries.

Compared to existing methods, the approach shows significant accuracy gains.

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.