Related papers: Dynamical systems and complex networks: A Koopman …
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
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 introductory guide to Koopman…
Koopman operators, since introduced by the French-born American mathematician Bernard Koopman in 1931, have been employed as a powerful tool for research in various scientific domains, such as ergodic theory, probability theory, geometry,…
This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A…
Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze…
Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network…
In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to…
Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering…
The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such…
Learning complex network dynamics is fundamental to understanding, modelling and controlling real-world complex systems. There are two main problems in the task of predicting the dynamic evolution of complex networks: on the one hand,…
Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the…
In this work, we develop a method to identify continuous-time nonlinear networked dynamics via the Koopman operator framework. The proposed technique consists of two steps: the first step identifies the neighbors of each node, and the…
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…
We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear…
Koopman operator theory is receiving increased attention due to its promise to linearize nonlinear dynamics. Neural networks that are developed to represent Koopman operators have shown great success thanks to their ability to approximate…
Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative…
This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…
In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of…
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…