  We propose a novel stochastic reduced-order model (SROM) for complex systems
by combining clustering and classification strategies. Specifically, the
distance and centroid of centroidal Voronoi tessellation (CVT) are redefined
according to the optimality of proper orthogonal decomposition (POD), thereby
obtaining a time-dependent generalized CVT, and each class can generate a set
of cluster-based POD (CPOD) basis functions. To learn the classification
mechanism of random input, the naive Bayes pre-classifier and clustering
results are applied. Then for a new input, the set of CPOD basis functions
associated with the predicted label is used to reduce the corresponding model.
Rigorous error analysis is shown, and a discussion in stochastic Navier-Stokes
equation is given to provide a context for the application of this model.
Numerical experiments verify that the accuracy of our SROM is improved compared
with the standard POD method.
