Nonlinear Correlation of POD and DMD Modal Coefficients in Reduced-Order Modeling of Flow Around a Cylinder in a Microchannel

Nonlinear correlations among modal coefficients enable interpretable reduced-order models (ROMs) for microfluidic flows. In this study, flow around a cylinder in a microchannel at Re = 100 is investigated using proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and POD + DMD. The sparse identification of nonlinear dynamics (SINDy) is employed to identify nonlinear correlations among modal coefficients. The results show that the first POD mode contains 33% of the total kinetic energy, and the first 14 modes capture 99.2% of the energy. A minimal ROM with only two degrees of freedom is constructed, in which the real and imaginary parts of active modal coefficients differ in phase by π/2 and their magnitude equals the vortex-shedding fundamental frequency (1.067 Hz). Among sparse regression algorithms, the FROLS method yields the sparsest representation (sparsity rate 0.05), whereas other methods give sparsity rate > 0.3. Reducing the temporal resolution from 0.01 to 0.1 increases the manifold dynamics coefficient error from 0% to 0.56%. Only the ROMs built from POD + DMD and DMD preserve essential kinematic resolution. The POD-based ROM fails to maintain correct energy levels over long-time integration. Therefore, the nonlinear correlation between POD + DMD modal coefficients is recommended for developing ROMs in microchannel flows when accuracy, interpretability, and stability are considered together.