Related papers: Operator is the Model
The Koopman operator plays a crucial role in analyzing the global behavior of dynamical systems. Existing data-driven methods for approximating the Koopman operator or discovering the governing equations of the underlying system typically…
We present KoopCast, a lightweight yet efficient model for trajectory forecasting in general dynamic environments. Our approach leverages Koopman operator theory, which enables a linear representation of nonlinear dynamics by lifting…
In this paper, we develop the Koopman operator theory for dynamical systems with symmetry. In particular, we investigate how the Koopman operator and eigenfunctions behave under the action of the symmetry group of the underlying dynamical…
We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data…
Koopman operators, since introduced by the French-born American mathematician Bernard Koopman in 1931, have been employed as a powerful tool for research in various scientific domains, such as ergodic theory, probability theory, geometry,…
We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables.…
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…
This paper introduces a reduced order modeling technique based on Koopman operator theory that gives confidence bounds on the model's predictions. It is based on a data-driven spectral decomposition of the Koopman operator. The reduced…
The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…
We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate the magnitude of the time-scale separation, and finally 3)…
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…
In this paper, we provide an algorithm for online computation of Koopman operator in real-time using streaming data. In recent years, there has been an increased interest in data-driven analysis of dynamical systems, with operator theoretic…
Controlling nonlinear dynamical systems remains a central challenge in a wide range of applications, particularly when accurate first-principle models are unavailable. Data-driven approaches offer a promising alternative by designing…
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 has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying linear function space representations of nonlinear dynamics from…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Offline reinforcement learning leverages large datasets to train policies without interactions with the environment. The learned policies may then be deployed in real-world settings where interactions are costly or dangerous. Current…
Nonlinear Negative Imaginary (NI) systems arise in various engineering applications, such as controlling flexible structures and air vehicles. However, unlike linear NI systems, their theory is not well-developed. In this paper, we propose…
In dynamic simulation of complete wheel loaders, one interesting aspect, specific for the working task, is the momentary power distribution between drive train and hydraulics, which is balanced by the operator. This paper presents the…
In data-driven modelling of complex dynamic processes, it is often desirable to combine different classes of models to enhance performance. Examples include coupled models of different fidelities, or hybrid models based on physical…