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

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

“…In present work, we employ maxent functions derived in Section 2 as bases for chaos expansions. Data-driven function approximation using maxent basis functions is discussed in detail in Deshpande and Bhattacharya (2019b). In this paper, we focus on the application of maxent basis functions for solution of stochastic differential equations.…”

“…The same basis nodes are used for function approximation in step one and chaos expansion in step two. The weights or coefficients associated with basis functions for function approximation are determined by the least squares solution as discussed in Deshpande and Bhattacharya (2019b).…”

“…6. However, as discussed in Deshpande and Bhattacharya (2019b), it should be noted that if the underlying functional form of a(∆) lies within the span of basis polynomials, then aPC based model will have similar, or perhaps even better accuracy the maxent model. But, for functions such as we considered here, which are difficult to approximate using polynomials, especially if the given data set is sparse, maxent based models perform better.…”

“…For the sake of completeness, maxent based polygonal interpolation is briefly reviewed in Section 2. Our recent work, Deshpande and Bhattacharya (2019b), discussed the data-driven function approximation using such maxent basis functions in the context of dynamics modeling. The results show that maxent based approach can model the unknown dynamics with good accuracy even if the available data set is sparse.…”