Data-driven Solution of Stochastic Differential Equations Using Maximum Entropy Basis Functions

Abstract: In this paper we present a data-driven approach for uncertainty propagation. In particular, we consider stochastic differential equations with parametric uncertainty. Solution of the differential equation is approximated using maximum entropy (maxent) basis functions similar to polynomial chaos expansions. Maxent basis functions are derived from available data by maximization of information-theoretic entropy, therefore, there is no need to specify basis functions beforehand. We compare the proposed maxent based approach with existing methods.