Concept

Composition operator

Related publications (18)

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...

2024

Data-Driven Control Synthesis using Koopman Operator: A Robust Approach

Alireza Karimi, Mert Eyuboglu, Nathan Russell Powell

This paper proposes a data-driven control design method for nonlinear systems that builds upon the Koopman operator framework. In particular, the Koopman operator is used to lift the nonlinear dynamics to a higher-dimensional space where the so-called obse ...

2024

Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques

Tobias Schneider, Omid Ashtari

Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational challenge, rendering many ...

Cambridge2023

Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation

Jan Sickmann Hesthaven, Nicolò Ripamonti, Cecilia Pagliantini

. High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of para ...

AMER MATHEMATICAL SOC2023

koopmans: An Open-Source Package for Accurately and Efficiently Predicting Spectral Properties with Koopmans Functionals

Nicola Marzari, Nicola Colonna, Edward Baxter Linscott, Ngoc Linh Nguyen, Giovanni Borghi, Riccardo De Gennaro, Andrea Ferretti

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise linearity conditio ...

Washington2023

Koopmans Spectral Functionals in Periodic Boundary Conditions

Nicola Marzari, Nicola Colonna, Edward Baxter Linscott, Riccardo De Gennaro

Koopmans spectral functionals aim to describe simultaneously ground-state properties and charged excitations of atoms, molecules, nanostructures, and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically ...

AMER CHEMICAL SOC2022

Spectral properties of extended systems from Koopmans-compliant functionals

Riccardo De Gennaro

Electronic-structure simulations have been impacting the study of materials properties thanks to the simplicity of density-functional theory, a method that gives access to the ground state of the system. Although very important, ground-state properties rep ...

EPFL2022

Bloch's theorem in orbital-density-dependent functionals: Band structures from Koopmans spectral functionals

Nicola Marzari, Nicola Colonna, Edward Baxter Linscott, Riccardo De Gennaro

Koopmans-compliant functionals provide an orbital-density-dependent framework for an accurate evaluation of spectral properties; they are obtained by imposing a generalized piecewise-linearity condition on the total energy of the system with respect to the ...

AMER PHYSICAL SOC2022

Koopman Analysis of Isolated Fronts and Solitons

A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyze nonlinear dynamical systems brings new strategies for prediction and control, w ...

2020

On Gaussian Process based Koopman Operator

Colin Neil Jones

Enabling analysis of non-linear systems in linear form, the Koopman operator has been shown to be a powerful tool for system identification and controller design. However, current data-driven methods cannot provide quantification of model uncertainty given ...

2020

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