Dynamic Mode Decomposition

Dynamic Mode Decomposition (DMD) is a data-driven technique used to analyze complex dynamical systems by decomposing them into a set of simpler, time-evolving modes. Current research focuses on improving DMD's accuracy and efficiency, particularly through the development of kernel-based methods, deep learning integrations, and variations like higher-order DMD (HODMD) and optimized DMD (OPT-DMD) to handle noise, non-uniform data, and high dimensionality. These advancements are enabling more accurate modeling and prediction across diverse fields, including fluid dynamics, atmospheric science, and even the analysis of neural network training dynamics and biological signals. The resulting reduced-order models offer significant computational advantages for real-time applications and enhanced interpretability of complex systems.