Related papers: Koopman Operator Applications in Signalized Traffi…
Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this…
In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant…
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…
This work continues the parametric investigation on the sampling nuances of the Dynamic Mode Decomposition (DMD) under the Koopman analysis. Through turbulent wakes, the investigation corroborated the generality of the universal convergence…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
In recent years, there has been a growing interest in data-driven approaches in physics, such as extended dynamic mode decomposition (EDMD). The EDMD algorithm focuses on nonlinear time-evolution systems, and the constructed Koopman matrix…
Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…
The present study focuses on a subject of significant interest in fluid dynamics: the identification of a model with decreased computational complexity from numerical code output using Koopman operator theory. A reduced-order modelling…
Dynamic mode decomposition (DMD) is a popular approach to analyzing and modeling fluid flows. In practice, datasets are almost always corrupted to some degree by noise. The vanilla DMD is highly noise-sensitive, which is why many…
We propose a novel method for forecasting the temporal evolution of probability distributions observed at discrete time points. Extending the Dynamic Probability Density Decomposition (DPDD), we embed distributional dynamics into…
Representation of a dynamical system in terms of simplifying modes is a central premise of reduced order modelling and a primary concern of the increasingly popular DMD (dynamic mode decomposition) empirical interpretation of Koopman…
Koopman mode decomposition (KMD) is a technique of nonlinear time-series analysis capable of decomposing data on complex spatio temporal dynamics into multiple modes oscillating with single frequencies, called the Koopman modes (KMs). We…
Dynamic mode decomposition (DMD) is a versatile approach that enables the construction of low-order models from data. Controller design tasks based on such models require estimates and guarantees on predictive accuracy. In this work, we…
This paper proposes a distributed model predictive control (DMPC) approach for an urban traffic network (UTN) system. The control objective is to minimize the traffic congestion and the total travel time spent (TTS) in each link. The…
Mixed vehicle platoons, comprising connected and automated vehicles (CAVs) and human-driven vehicles (HDVs), hold significant potential for enhancing traffic performance. However, most existing control strategies assume linear system…
We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate the magnitude of the time-scale separation, and finally 3)…
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…
We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band…
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…
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…