Physics-regulated dynamic mode decomposition for two-dimensional laminar flow past square cylinder

Physics-regulated dynamic mode decomposition (PRDMD) is proposed as an improved framework over conventional dynamic mode decomposition (DMD), which allows robust and accurate predictions for two-dimensional laminar flow around a square cylinder. PRDMD addresses the limitations of the conventional DMD by incorporating physical laws, such as mass and momentum conservation, as regularizers, which struggle in noisy environments and with limited training data. To handle non-linear terms, such as convection terms as regularizers, this study treats these terms as independent features to be considered. The proposed method demonstrates significant improvements in noise robustness and physical consistency, reconstructing the flow field with reduced errors even in high-noise scenarios. Comparative analyses demonstrate the ability of PRDMD to reconstruct the vorticity field while adhering to the governing equations. It outperforms DMD in both the reconstruction and prediction phases. In addition, PRDMD maintains the stability of the eigenvalues, ensuring consistent oscillatory dynamics over extended time horizons. These findings highlight its potential as a reliable reduced-order modeling technique for complex fluid dynamics applications. It is particularly effective in scenarios with data scarcity and measurement uncertainty.