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

TL;DR

This paper introduces a stochastic reduced-order model that combines clustering, classification, and POD techniques to efficiently simulate complex, time-dependent systems with improved accuracy over traditional methods.

Contribution

The paper develops a novel SROM by redefining CVT based on POD optimality and integrating a classification mechanism for better model reduction in stochastic systems.

Findings

Enhanced accuracy over standard POD methods.

Effective classification-based model reduction.

Application demonstrated on stochastic Navier-Stokes equations.

Abstract

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.