2023/12/13 by Gowtham S Seenivasaharagavan, Milan Korda, Seenivasaharagavan, Gowtham S +5
Engineering · Physics and Astronomy · #Data Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Vibration Analysis #Machine Fault Diagnosis Techniques #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2312.08278
openalex publication_date 2023/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the central idea is to preserve a fundamental property of the Koopman operator: linearity. This work augments DMD by preserving additional properties like functional relationships between observables and consistency along geometric invariants. The first set of constraints provides a framework for understanding DMD variants like Higher-order DMD and Affine DMD. The latter set guarantees the estimation of Koopman eigen-functions with eigen-value 1, whose level sets are known to delineate invariant sets. These benefits are realized with only a minimal increase in computational cost, primarily due to the linearity of constraints.