Characterizing complex flows using adaptive sparse dynamic mode decomposition with error approximation

Summary Dynamic mode decomposition (DMD) is a powerful data‐driven method for analyzing the coherent structures of dynamical systems. This work develops an adaptive sparse DMD with error approximation for the sparse reconstruction of complex flow fields. First, we propose a new sparse DMD model by redefining the penalty function, where adaptive weights are assigned to penalize different DMD modes. With the adaptive weights, the sparse DMD model is more capable of extracting important DMD modes and discarding unimportant ones. Second, we develop a novel error prediction model for the proposed sparse DMD. The key idea is to construct a multiple regression model between the sparse model and its error by employing the partial least squares regression. The error of the sparse DMD model can be reduced by integrating the error prediction model. Finally, we assess the proposed method by means of test cases, including a nonlinear parameterized function, a cylinder bundle flow, and the transient state of square cylinder flow. The results show that the proposed method can be used to capture the dominant modes and substantially increase the accuracy of flow reconstruction. We present an adaptive sparse DMD model (ASP‐DMD) for extracting the dominant modes. Then, we construct an error prediction model for ASP‐DMD (ASP‐DMD‐opt) by using the partial least squares regression. We also apply the proposed model to the complex flows, including a cylinder bundle flow and the transient state of square cylinder flow.