Related papers: CKNet: A Convolutional Neural Network Based on Koo…

Continuous monitoring of the spatio-temporal dynamic behavior of critical infrastructure networks, such as the power systems, is a challenging but important task. In particular, accurate and timely prediction of the (electro-mechanical)…

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…

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to…

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…

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…

Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…

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…

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…

Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…

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…

Koopman operator has been recognized as an ongoing data-driven modeling method for vehicle dynamics which lifts the original state space into a high-dimensional linear state space. The deep neural networks (DNNs) are verified to be useful…

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…

This paper presents DeepKoCo, a novel model-based agent that learns a latent Koopman representation from images. This representation allows DeepKoCo to plan efficiently using linear control methods, such as linear model predictive control.…

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…

Autonomous driving has attracted lots of attention in recent years. An accurate vehicle dynamics is important for autonomous driving techniques, e.g. trajectory prediction, motion planning, and control of trajectory tracking. Although…

Nonlinearity plays a crucial role in deep neural networks. In this paper, we investigate the degree to which the nonlinearity of the neural network is essential. For this purpose, we employ the Koopman operator, extended dynamic mode…

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…

Learning complex network dynamics is fundamental to understanding, modelling and controlling real-world complex systems. There are two main problems in the task of predicting the dynamic evolution of complex networks: on the one hand,…

This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the controller performance can deteriorate if the modeling error…

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…