Related papers: Variance representations and convergence rates for…
We exploit the relationship between the stochastic Koopman operator and the Kolmogorov backward equation to construct importance sampling schemes for stochastic differential equations. Specifically, we propose using eigenfunctions of the…
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…
Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. This turns the nonlinear problem into a linear,…
The estimation of equations from data is of interest in physics. One of the famous methods is the sparse identification of nonlinear dynamics (SINDy), which utilizes sparse estimation techniques to estimate equations from data. Recently, a…
We consider the identification problems for nonlinear dynamical systems. An explicit sample complexity bound in terms of the number of data points required to recover the models accurately is derived. Our results extend recent sample…
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.…
This paper presents a data-driven method for constructing a Koopman linear model based on the Direct Encoding (DE) formula. The prevailing methods, Dynamic Mode Decomposition (DMD) and its extensions are based on least squares estimates…
The Koopman operator provides an infinite-dimensional linear description of nonlinear dynamical systems that can be leveraged in the context of stability analysis. In particular, Lyapunov functions can be obtained in a systematic way via…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
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…
Dynamic Mode Decomposition (DMD) has received increasing research attention due to its capability to analyze and model complex dynamical systems. However, it faces challenges in computational efficiency, noise sensitivity, and difficulty…
This paper derives conditions under which Model Predictive Control (MPC) with terminal conditions, using a data-driven surrogate model as a prediction model, asymptotically stabilizes the plant despite approximation errors. In particular,…
Empirical divergence maximization (EDM) refers to a recently proposed strategy for estimating f-divergences and likelihood ratio functions. This paper extends the idea to empirical vector quantization where one seeks to empirically derive…
In this paper, we present a convergence rate analysis for the inexact Krasnosel'skii-Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration-complexity…
In this paper we consider the Koopman operator associated with the discrete and the continuous time random dynamical system (RDS). We provide results that characterize the spectrum and the eigenfunctions of the stochastic Koopman operator…
Koopman operator theory is a key tool in data assimilation of complex dynamical systems, with the potential to be applied to multimodal data. We formulate the problem of learning Koopman eigenfunctions from observations at arbitrary,…
This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…
Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this work, we attempt to provide a consistent framework through Koopman theory and its related…
Analyzing the long-term behavior of high-dimensional nonlinear dynamical systems remains a significant challenge. While the Koopman operator framework provides a powerful global linearization tool, current methods for approximating its…
We propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate $O(1/T)$ and $O(\frac{1}{\log…