2024/09/24 by Ningxin Liu, Liu, Ningxin, Shiyang Liu +5 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #FOS: Electrical engineering #FOS: Mathematics #Flow Measurement and Analysis #Model Reduction and Neural Networks #Probability (math.PR) #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2410.02815
openalex publication_date 2024/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dynamic mode decomposition (DMD) is a data-driven method of extracting spatial-temporal coherent modes from complex systems and providing an equation-free architecture to model and predict systems. However, in practical applications, the accuracy of DMD can be limited in extracting dynamical features due to sensor noise in measurements. We develop an adaptive method to constantly update dynamic modes and eigenvalues from noisy measurements arising from discrete systems. Our method is based on the Ensemble Kalman filter owing to its capability of handling time-varying systems and nonlinear observables. Our method can be extended to non-autonomous dynamical systems, accurately recovering short-time eigenvalue-eigenvector pairs and observables. Theoretical analysis shows that the estimation is accurate in long term data misfit. We demonstrate the method on both autonomous and non-autonomous dynamical systems to show its effectiveness.