相关论文: Mori-Zwanzig latent space Koopman closure for nonl…
Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of…
A Transformer-based Koopman autoencoder is proposed for linearizing Fisher's reaction-diffusion equation. The primary focus of this study is on using deep learning techniques to find complex spatiotemporal patterns in the reaction-diffusion…
The Koopman operator provides a powerful framework for data-driven analysis of dynamical systems. In the last few years, a wealth of numerical methods providing finite-dimensional approximations of the operator have been proposed (e.g.…
The Mori-Zwanzig projection operator formalism is a powerful method for the derivation of mesoscopic and macroscopic theories based on known microscopic equations of motion. It has applications in a large number of areas including fluid…
Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features…
The dynamic complexity of robots and mechatronic systems often pertains to the hybrid nature of dynamics, where governing equations consist of heterogenous equations that are switched depending on the state of the system. Legged robots and…
We consider Koopman operator theory in the context of nonlinear infinite-dimensional systems, where the operator is defined over a space of bounded continuous functionals. The properties of the Koopman semigroup are described and a…
Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…
Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…
This paper presents a methodology to achieve lower-dimensional Koopman quasi-linear representations of nonlinear system dynamics using Koopman generalized eigenfunctions. The proposed approach considers the analytically derived Koopman…
Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through Koopman operator analysis. However, computing Koopman eigen pairs for high-dimensional observable data can be…
The Koopman operator is beneficial for analyzing nonlinear and stochastic dynamics; it is linear but infinite-dimensional, and it governs the evolution of observables. The extended dynamic mode decomposition (EDMD) is one of the famous…
Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast…
Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…
Reduced Order Models (ROMs) of complex, nonlinear dynamical systems often require closure, which is the process of representing the contribution of the unresolved physics on the resolved physics. The Mori-Zwanzig (M-Z) procedure allows one…
In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, Proper Orthogonal Decomposition (POD)…
Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control…