Related papers: Dynamic Mode Decomposition for Continuous Time Sys…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the…
This paper presents a data-driven approach for designing state observers for continuous-time nonlinear systems, where an extended dynamic mode decomposition (EDMD) procedure is used to identify an approximate linear lifted model. Since such…
Dynamic Mode Decomposition (DMD) has received increasing research attention due to its capability to analyze and model complex dynamical systems. However, it faces challenges in computational efficiency, noise sensitivity, and difficulty…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…
We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized Dynamic-Mode Decomposition (JDMD), offers improved sample efficiency over traditional Koopman approaches based…
Dynamic Mode Decomposition (DMD) is a data-driven modeling tool that generates a model from spatio-temporal data. The data needs to be as clean as possible for DMD to come up with a faithful model. We review a few data-filtering methods to…
We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing methods, SDMD explicitly incorporates sampling time into its…
With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a…
The Koopman operator enables the analysis of nonlinear dynamical systems through a linear perspective by describing time evolution in the infinite-dimensional space of observables. Here this formalism is applied to shear flows, specifically…
This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman…
Koopman operators and transfer operators represent dynamical systems through their induced linear action on vector spaces of observables, enabling the use of operator-theoretic techniques to analyze nonlinear dynamics in state space. The…
We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…
The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. This is entirely a data-driven approach that extracts all necessary information from data snapshots which are commonly supposed to be sampled…
The Koopman operator provides a powerful framework for data-driven analysis of dynamical systems. In the last few years, a wealth of numerical methods providing finite-dimensional approximations of the operator have been proposed (e.g.…
Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…
Conventional generators have been retired or replaced by renewable energy because of the utility long-standing goals. However, instead of decommissioning the entire plant, the rotating mass can be utilized as a storage unit to mitigate the…
This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that DMD and other standard data-driven methods face a fundamental difficulty…
Linear dynamical systems are fully characterized by their eigenspectra, accessible directly from the generator of the dynamics. For nonlinear systems governed by partial differential equations, no equivalent theory exists. We introduce Lie…