Related papers: Koopman analysis of quantum systems
The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of…
Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in…
The theory of dual control was introduced more than seven decades ago. Although it has provided rich insights to the fields of control, estimation, and system identification, dual control is generally computationally prohibitive. In recent…
Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide…
Predictive control of power electronic systems always requires a suitable model of the plant. Using typical physics-based white box models, a trade-off between model complexity (i.e. accuracy) and computational burden has to be made. This…
We present a method to obtain a data-driven Koopman operator-based model that adapts itself during operation and can be straightforwardly used for the controller and observer design. The adaptive model is able to accurately describe…
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 recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation…
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 offers a rigorous treatment of dynamics and has been emerging as an alternative modeling and learning-based control method across various robotics sub-domains. Due to its ability to represent nonlinear dynamics as a…
Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…
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…
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…
Conserved quantities, i.e. constants of motion, are critical for characterizing many dynamical systems in science and engineering. These quantities are related to underlying symmetries and they provide fundamental knowledge about physical…
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 operator lifts nonlinear dynamical systems into a functional space of observables, where the dynamics are linear. In this paper, we provide three different Koopman representations for hybrid systems. The first is specific to…
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of classical mechanics. The main advantage…
Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…
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…