Clustering-Based Reduced-Order Model Initialized by Proper Orthogonal Decomposition and Its Application to Convective Flow Problems

Proper Orthogonal Decomposition (POD) methods, which primarily rely on linear dimensionality reduction, often fail to capture critical features in complex nonlinear flows. Conversely, while clustering methods excel in nonlinear feature extraction, they are limited by instability in cluster center initialization and inefficiencies in modal sorting, thereby restricting their usability in reduced-order modeling (ROM). To address these challenges, this study introduces the Clustering-based Reduced-Order Model (C-POD), which integrates POD preprocessing to stabilize cluster center selection and employs an Entropy-Controlled Euclidean-to-Probability Mapping (ECEPM) technique to refine modal sorting. The efficacy of C-POD is demonstrated through applications to Burgers’ equation and a cylinder wake flow case. Numerical results reveal that C-POD achieves superior dimensionality reduction accuracy compared to POD, with primary modes capturing more of the time-dependent dynamics and higher-order modes exhibiting enhanced physical interpretability. Moreover, ECEPM-based low-order modes significantly improve C-POD’ s accuracy in low-dimensional representations. The method’s low-order accuracy advantage is further substantiated through an inverse problem, where sparse sensor data enable the real-time reconstruction of the cylinder wake vorticity field. Results indicate that the Gappy C-POD method attains a 19.75% improvement in reconstruction accuracy and a 13.4% enhancement in the lower bound of reconstruction capability relative to Gappy POD. Additionally, C-POD maintains high reconstruction accuracy even at higher modal orders, making it particularly well-suited for reconstructing complex nonlinear system fields. This study offers compelling evidence supporting the potential application of the clustering-based C-POD framework to complex flow problems, thereby providing new insights into reduced-order modeling of nonlinear systems.