A Study on Gramian Closures in Bimodal Phenomena

Abstract This work analyzes the prediction quality of Gramian closures using a strongly bimodal distribution modeled as the superposition of two Gaussian functions. In [1], a new class of hyperbolic closures based on orthogonal polynomials named Gramian and extended Gramian closures has been introduced. These new closures are compared with Grad and the maximum entropy closures in terms of approximation quality. Numerical experiments show that the extended Gramian closure achieves competitive accuracy with the maximum entropy approach, particularly for even-order moments.