Pre-classification based stochastic reduced-order model for time-dependent complex system

Abstract

We propose a novel stochastic reduced-order model (SROM) for complex systems by combining statistical analysis tools. Based on the generalizability of distance in the centroidal Voronoi tessellation (CVT) method and the minimization of projection error in proper orthogonal decomposition (POD), we define a time-dependent generalized CVT clustering. Each generalized centroid corresponds to a set of cluster-based POD (CPOD) basis functions. Then, using the clustering results as the training dataset, the classification mechanism of the system input can be obtained by applying the naive Bayesian method. For a given input sample, the predicted label obtained by the classifier is used to determine a set of CPOD basis functions for model reduction. Rigorous error analysis is shown, and a discussion of the Navier-Stokes equation with random parameters is given to provide a context for the application of this SROM. Numerical experiments verify that the accuracy of our SROM is improved compared with the standard POD method.