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The Koopman framework is a popular approach to transform a finite dimensional nonlinear system into an infinite dimensional, but linear model through a lifting process, using so-called observable functions. While there is an extensive…

Systems and Control · Electrical Eng. & Systems 2023-12-18 Lucian Cristian Iacob , Maarten Schoukens , Roland Tóth

Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design…

Soft Condensed Matter · Physics 2024-11-26 Atoosa Parsa , James Bagrow , Corey S. O'Hern , Rebecca Kramer-Bottiglio , Josh Bongard

Time-dependent orbital-free DFT is an efficient method for calculating the dynamic properties of large scale quantum systems due to the low computational cost compared to standard time-dependent DFT. We formalize this method by mapping the…

Chemical Physics · Physics 2021-06-09 Kaili Jiang , Michele Pavanello

The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…

Condensed Matter · Physics 2009-10-22 O. K. Vorov , A. V. Vagov

The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use of electronic structure theories that account for both multi-reference as well as dynamic correlation effects. A variety…

Chemical Physics · Physics 2023-01-03 Jan-Niklas Boyn , David A. Mazziotti

We propose a general machine learning-based framework for building an accurate and widely-applicable energy functional within the framework of generalized Kohn-Sham density functional theory. To this end, we develop a way of training…

Computational Physics · Physics 2020-12-14 Yixiao Chen , Linfeng Zhang , Han Wang , E Weinan

Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of the time evolution of observable quantities. Recent methods…

Dynamical Systems · Mathematics 2025-06-06 Nicolas Boullé , Matthew J. Colbrook

We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolution of observables, Koopman operators transform complex…

Dynamical Systems · Mathematics 2024-12-04 Matthew J. Colbrook , Catherine Drysdale , Andrew Horning

The design of better exchange-correlation functionals for Density Functional Theory (DFT) is a central challenge of modern electronic structure theory. However, current developments are limited by the mathematical form of the functional,…

Chemical Physics · Physics 2024-08-19 Kyle Bystrom , Boris Kozinsky

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging as an alternative modeling and learning-based control method across various robotics sub-domains. Due to its ability to represent nonlinear dynamics as a…

In this paper, we propose a generic and systematic approach for study of the electronic structure for atoms or molecules. In particular, we address the issue of single particle states, or orbitals, which should be one of the most important…

Chemical Physics · Physics 2007-05-23 Liqiang Wei

We present a data-driven method for spectral analysis of the Koopman operator based on direct construction of the pseudo-resolvent from time-series data. Finite-dimensional approximation of the Koopman operator, such as those obtained from…

Dynamical Systems · Mathematics 2026-02-23 Yuanchao Xu , Itsushi Sakata , Isao Ishikawa

We introduce a framework for resolving electron-hole dynamics within wavefunction-based multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory. Central to this framework is a time-domain generalization of the extended Koopmans'…

Atomic Physics · Physics 2026-01-13 Zhao-Han Zhang , Yang Li , Himadri Pathak , Takeshi Sato , Kenichi L. Ishikawa , Feng He

In orbital-free density functional theory the kinetic potential (KP), the functional derivative of the kinetic energy density functional, appears in the Euler equation for the electron density and may be more amenable to simple…

Other Condensed Matter · Physics 2015-05-13 Jeng-Da Chai , Vincent L. Ligneres , Gregory Ho , Emily A. Carter , John D. Weeks

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…

Machine Learning · Computer Science 2025-05-28 Yuanchao Xu , Kaidi Shao , Nikos Logothetis , Zhongwei Shen

Quantum mechanical methods based on the density functional theory (DFT) offer a realistic possibility of first-principles design of organic donor-acceptor systems and engineered band-gap materials. This promise is contingent upon the…

Chemical Physics · Physics 2013-12-03 Marcin Modrzejewski , Grzegorz Chałasiński , Małgorzata M. Szczęśniak

The practical success of density functional theory (DFT) is largely credited to the Kohn-Sham approach, which enables the exact calculation of the non-interacting electron kinetic energy via an auxiliary noninteracting system. Yet, the…

Computational Physics · Physics 2025-03-21 Sangita Majumdar , Zekun Shi , Giovanni Vignale

Recent advances in X-ray free-electron laser diagnostics have enabled direct probing of the electronic structure under extreme pressures and temperatures, such as those encountered in stellar interiors and inertial confinement fusion…

As a continuation of our previous work \cite{KV2} the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces…

Complex Variables · Mathematics 2017-04-18 Gergely Kiss , Csaba Vincze

Orbital-free Density Functional Theory (OF-DFT) has been used when studying atoms, molecules and solids. In nuclear physics, there has been basically no application of OF-DFT so far, as the Density Functional Theory (DFT) has been widely…

Nuclear Theory · Physics 2023-08-03 Gianluca Colo' , Kouichi Hagino