Related papers: Learning Hamiltonian neural Koopman operator and s…
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman…
Designing neural networks within a Hamiltonian framework offers a principled way to ensure that conservation laws are respected in physical systems. While promising, these capabilities have been largely limited to discrete, analytically…
This paper explores a simple question: can we model the internal transformations of a neural network using dynamical systems theory? We introduce Koopman autoencoders to capture how neural representations evolve through network layers,…
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…
The mathematical properties and data-driven learning of the Koopman operator, which represents nonlinear dynamics as a linear mapping on a properly defined functional spaces, have become key problems in nonlinear system identification and…
Learning dexterous manipulation skills presents significant challenges due to complex nonlinear dynamics that underlie the interactions between objects and multi-fingered hands. Koopman operators have emerged as a robust method for modeling…
With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a…
The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to a series of computational techniques for numerical solutions. Although numerous latest advances are accomplished in developing neural…
The Koopman operator has gained significant attention in recent years for its ability to verify evolutionary properties of continuous-time nonlinear systems by lifting state variables into an infinite-dimensional linear vector space. The…
We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optimization algorithm and the loss function. Using this induced…
We develop a Koopman operator framework for studying the {computational properties} of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ``Koopman…
The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…
The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
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…
Learning tractable linear representations of nonlinear dynamical systems via Koopman operator theory is often hindered by dictionary selection, temporal memory encoding, and numerical ill-conditioning. Inspired by Reservoir Computing (RC)…
Mobile robot navigation can be challenged by system uncertainty. For example, ground friction may vary abruptly causing slipping, and noisy sensor data can lead to inaccurate feedback control. Traditional model-based methods may be limited…
The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept$\unicode{x2013}$representing highly nonlinear dynamical systems by infinite-dimensional linear…
Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets,…