Related papers: Data-driven Modeling of Granular Chains with Moder…

In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust…

Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of…

Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original…

Koopman theory asserts that a nonlinear dynamical system can be mapped to a linear system, where the Koopman operator advances observations of the state forward in time. However, the observable functions that map states to observations are…

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 been useful in…

This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…

The purpose of this article is to provide a perspective -- admittedly, a rather subjective one -- of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of…

The dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such…

A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…

Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…

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…

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.…

Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…

This study introduces a data-driven twin modeling framework based on modern Koopman operator theory, offering a significant advancement over classical modal decomposition by accurately capturing nonlinear dynamics with reduced complexity…

In many scenarios, it is necessary to monitor a complex system via a time-series of observations and determine when anomalous exogenous events have occurred so that relevant actions can be taken. Determining whether current observations are…

Driven granular media constitute model systems in out-of-equilibrium statistical physics. By assimilating the motions of granular particles to those of atoms, by analogy, one can obtain macroscopic equivalent of phase transitions. Here, we…

Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. This paper addresses the use of a…

The Koopman framework proposes a linear representation of finite-dimensional nonlinear systems through a generally infinite-dimensional globally linear embedding. Originally, the Koopman formalism has been derived for autonomous systems. In…

Stabilization, disturbance rejection, and control of optical beams and optical spots are ubiquitous problems that are crucial for the development of optical systems for ground and space telescopes, free-space optical communication…

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…