Koopman Spectral Analysis from Noisy Measurements based on Bayesian Learning and Kalman Smoothing
Koopman spectral analysis plays a crucial role in understanding and modeling nonlinear dynamical systems as it reveals key system behaviors and long-term dynamics. However, the presence of measurement noise poses a significant challenge to accurately extracting spectral properties. In this work, we propose a robust method for identifying the Koopman operator and extracting its spectral characteristics in noisy environments. To address the impact of noise, our approach tackles an identification problem that accounts for both systematic errors from finite-dimensional approximations and measurement noise in the data. By incorporating Bayesian learning and Kalman smoothing, the method simultaneously identifies the Koopman operator and estimates system states, effectively decoupling these two error sources. The method's efficiency and robustness are demonstrated through extensive experiments, showcasing its accuracy across varying noise levels.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability
The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have…
Variational InferenceThe mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems
Koopman operators globally linearize nonlinear dynamical systems and their spectral information is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. However, Koopman operators are infinit…
Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation
Koopman theory promises linear structure in nonlinear dynamics, but numerical Koopman spectra are easy to compute and hard to trust. A finite EDMD matrix always has eigenvalues; the problem is that many of them may have …
Temporally-Consistent Koopman Autoencoders for Forecasting Dynamical Systems
Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural net…
Dimensionality ReductionAn Introductory Guide to Koopman Learning
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introducto…