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The mathematical properties and data-driven learning of the Koopman operator, which represents nonlinear dynamics as a linear mapping on a properly defined functional spaces, have become key problems in nonlinear system identification and…
In the paper, we consider the problem of robust approximation of transfer Koopman and Perron-Frobenius (P-F) operators from noisy time series data. In most applications, the time-series data obtained from simulation or experiment is…
We present a comparative study of several dynamical systems of increasing complexity, namely, the logistic map with additive noise, one, two and many globally-coupled standard maps, and the Hamiltonian Mean Field model (i.e., the classical…
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
This paper addresses a learning problem for nonlinear dynamical systems with incorporating any specified dissipativity property. The nonlinear systems are described by the Koopman operator, which is a linear operator defined on the…
Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to…
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…
In this paper, we leverage Koopman mode decomposition to analyze the nonlinear and high-dimensional climate systems acting on the observed data space. The dynamics of atmospheric systems are assumed to be equation-free, with the linear…
With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on…
It is sometimes difficult to achieve a complete observation for a full set of observables, and partial observations are necessary. For deterministic systems, the Mori-Zwanzig formalism provides a theoretical framework for handling partial…
Controlling nonlinear dynamical systems remains a central challenge in a wide range of applications, particularly when accurate first-principle models are unavailable. Data-driven approaches offer a promising alternative by designing…
Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…
Quantum van der Pol oscillators are driven-dissipative systems displaying quantum synchronization phenomena. When forced by a squeezed drive, the frequency adjusts to half of the forcing displaying multiple preferred phases. Here we analyze…
Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…
The widely used RED (Regularization-by-Denoising) framework uses pretrained denoisers as implicit regularizers for model-based reconstruction. Although RED generally yields high-fidelity reconstructions, the use of black-box denoisers can…
This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique…
We employ the framework of the Koopman operator and dynamic mode decomposition to devise a computationally cheap and easily implementable method to detect transient dynamics and regime changes in time series. We argue that typically…