Related papers: Toeplitz Based Spectral Methods for Data-driven Dy…
A new approach to data-driven discovery of Koopman eigenfunctions without a pre-defined set of basis functions is proposed. The approach is based on a reference trajectory, for which the Koopman mode amplitudes are first identified, and the…
Analyzing the spectral properties of the Koopman operator is crucial for understanding and predicting the behavior of complex stochastic dynamical systems. However, the accuracy of data-driven estimation methods, such as Extended Dynamic…
By considering an empirical approximation, and a new class of operators that we will call walking operators, we construct, for any positive ND-toeplitz matrix, an infinite in all dimensions matrix, for which the inverse approximates the…
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…
In this work, we consider a state estimation problem for large-scale nonlinear processes in the absence of first-principles process models. By exploiting process operation data, both process modeling and state estimation design are…
We propose a new method to recover global information about a network of interconnected dynamical systems based on observations made at a small number (possibly one) of its nodes. In contrast to classical identification of full graph…
A numerical framework is proposed for identifying partial differential equations (PDEs) governing dynamical systems directly from their observation data using Chebyshev polynomial approximation. In contrast to data-driven approaches such as…
Observable operator models (OOMs) and related models are one of the most important and powerful tools for modeling and analyzing stochastic systems. They exactly describe dynamics of finite-rank systems and can be efficiently and…
This work presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to…
We study nonlinear dynamics of the Earth's tropical climate system. For that, we apply a recently developed technique for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. The method…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…
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…
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…
Achieving rapid and time-deterministic stabilization for complex systems characterized by strong nonlinearities and parametric uncertainties presents a significant challenge. Traditional model-based control relies on precise system models,…
The Koopman operator enables the analysis of nonlinear dynamical systems through a linear perspective by describing time evolution in the infinite-dimensional space of observables. Here this formalism is applied to shear flows, specifically…
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.…
We introduce an encoder-only approach to learn the evolution operators of large-scale non-linear dynamical systems, such as those describing complex natural phenomena. Evolution operators are particularly well-suited for analyzing systems…
Toeplitz matrices arise naturally in harmonic analysis, operator theory, and numerical analysis. In this note we investigate Toeplitz matrices whose coefficients depend on the matrix size through a scaled kernel $a_k=f(k/n)$. We show that…
Data-driven safety verification of robotic systems often relies on zonotopic reachability analysis due to its scalability and computational efficiency. However, for nonlinear systems, these methods can become overly conservative, especially…
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…