Localized Dynamic Mode Decomposition with Temporally Adaptive Segmentation

Abstract. Dynamic mode decomposition (DMD) is a widely used data-driven method for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this limitation, we propose a localized DMD (LDMD) framework that improves prediction performance by integrating DMD’s strong linear forecasting capabilities with time-domain segmentation techniques. In this framework, the temporal domain is segmented into multiple sub-intervals, within which snapshot matrices are constructed and localized predictions are performed. We first present the localized DMD method with predefined segmentation, and then explore an adaptive segmentation strategy to further enhance computational efficiency and prediction robustness. Furthermore, we conduct an error analysis that provides the upper bound of the local and global truncation error for the proposed framework. The effectiveness of LDMD is demonstrated on four benchmark problems—Burgers’, Allen–Cahn, nonlinear Schrödinger, and Maxwell’s equations. Numerical results show that LDMD significantly enhances long-term predictive accuracy while preserving high computational efficiency.