A snapshot difference and amplitude optimization based dynamic mode decomposition method for reconstruction and prediction of flow fields

Dynamic mode decomposition (DMD) is extensively used in fluid dynamics to identify dominant flow structures and facilitate flow reconstruction and prediction. Conventional DMD, however, builds temporal snapshot matrices based exclusively on state variables at individual time instants, which often inadequately captures the behavior of localized or complex flows. To overcome this limitation, this study proposes an enhanced DMD technique that incorporates time-delay embedding by using difference values between state variables at consecutive time steps as the building blocks of the snapshot matrix. This approach not only retains instantaneous flow field information but also emphasizes temporal change characteristics, thereby improving the analytical capability of DMD. Moreover, a modal amplitude optimization procedure is integrated to increase the precision of reconstruction and prediction. The proposed method is validated on three test cases with increasing complexity and diverse backgrounds. Results show that the modified method significantly enhances the robustness and reconstruction accuracy of DMD, indicating its improved reliability for practical fluid dynamics applications.