MATLAB Implementation of Proper Orthogonal Decomposition (POD) Code

The MATLAB implementation of Proper Orthogonal Decomposition (POD) provides an efficient computational framework for reducing the dimensionality of large datasets while preserving critical patterns and essential information. This implementation utilizes Singular Value Decomposition (SVD) as its core mathematical foundation, where the data matrix is decomposed into orthogonal modes representing dominant patterns in the dataset. The code is particularly valuable in computational fluid dynamics applications, where extensive simulation or experimental data require efficient analysis. The algorithm identifies coherent structures and dominant modes of variation through eigenvalue decomposition of the covariance matrix, extracting the most significant features for further reduced-order modeling. Key functions in this implementation include data preprocessing, covariance matrix computation, eigenvalue decomposition, and mode selection based on energy criteria. The code structure allows customization of tolerance thresholds for mode selection and can be integrated with other dimensionality reduction techniques like Dynamic Mode Decomposition (DMD) for comprehensive data analysis. Researchers can modify the implementation to handle specific dataset characteristics, including time-series data and spatial field data. The modular design facilitates integration with visualization tools for mode inspection and validation. This POD implementation serves as a fundamental tool for extracting meaningful patterns from complex, high-dimensional datasets across various engineering and scientific domains.