Related papers: Learning dynamical systems: an example from open q…
In this paper, we propose a novel algorithm for learning the Koopman operator of a dynamical system from a \textit{small} amount of training data. In many applications of data-driven modeling, e.g. biological network modeling,…
Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…
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…
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…
This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We…
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…
Soft robots are challenging to model and control as inherent non-linearities (e.g., elasticity and deformation), often requires complex explicit physics-based analytical modeling (e.g., a priori geometric definitions). While machine…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…
The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under…
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…
We present a novel approach to shared control of human-machine systems. Our method assumes no a priori knowledge of the system dynamics. Instead, we learn both the dynamics and information about the user's interaction from observation…
The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. However, existing data-driven approaches to learning the Koopman operator rely on batch data. In this work, we present…
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…
We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their…
This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman…
Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…
Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in…