Koopman Mode Decomposition

Koopman mode decomposition is a data-driven technique used to analyze complex nonlinear dynamical systems by linearizing them through the Koopman operator. Current research focuses on improving the accuracy and robustness of algorithms like Dynamic Mode Decomposition (DMD) and its variants (e.g., extended DMD, kernelized DMD), particularly when dealing with limited data, stochastic systems, and high-dimensional data. These advancements enable the extraction of interpretable spatiotemporal patterns from diverse datasets, leading to improved forecasting and a deeper understanding of underlying dynamics in applications ranging from fluid mechanics and power grids to neuroscience. The rigorous development of algorithms with convergence guarantees and error control is a key trend, enhancing the reliability and applicability of Koopman-based analysis.