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Mathematics > Numerical Analysis

arXiv:2204.11151 (math)
[Submitted on 23 Apr 2022]

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

Authors:Meixin Xiong, Liuhong Chen, Ju Ming, Zhiwen Zhang
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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.
Comments: 25 pages, 16 figures and 6 tables
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2204.11151 [math.NA]
  (or arXiv:2204.11151v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2204.11151

Submission history

From: Meixin Xiong [view email]
[v1] Sat, 23 Apr 2022 23:35:01 UTC (1,497 KB)
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