Related papers: koopmans: an open-source package for accurately an…

We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which…

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…

We present a new theory for partitioning simulations of periodic and solid-state systems into physically sound atomic contributions at the level of Kohn-Sham density functional theory. Our theory is based on spatially localized linear…

We present a parallel data-driven strategy to identify finite-dimensional functional spaces invariant under the Koopman operator associated to an unknown dynamical system. We build on the Symmetric Subspace Decomposition (SSD) algorithm, a…

The performance of density functional theory depends largely on the approximation applied for the exchange functional. We propose here a novel screened exchange potential for semiconductors, with parameters based on the physical properties…

Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-scale spatial…

The piecewise linearity condition on the total energy with respect to the total magnetization of finite quantum systems is derived, using the infinite-separation-limit technique. This generalizes the well-known constancy condition, related…

We present a novel route to constructing cost-efficient semi-empirical approximations for the non-additive kinetic energy in subsystem density functional theory. The developed methodology is based on the use of Slater determinants composed…

Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…

Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for calculating various properties of solids as, for instance, the total energy, the electron density, or the electronic band structure. The KS-DFT method leads to…

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In…

The systematic underestimation of band gaps is one of the most fundamental challenges in semilocal density functional theory (DFT). In addition to hindering the application of DFT to predicting electronic properties, the band gap problem is…

Koopman operator theory provides a global linear representation of nonlinear dynamics and underpins many data-driven methods. In practice, however, finite-dimensional feature spaces induced by a user-chosen dictionary are rarely invariant,…

We developed a general framework for hybrid quantum-classical computing of molecular and periodic embedding approaches based on an orbital space separation of the fragment and environment degrees of freedom. We demonstrate its potential by…

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 analyse nonlinear dynamical systems brings new strategies for…

Nonlinear ordinary differential equations can rarely be solved analytically. Koopman operator theory provides a way to solve nonlinear systems by mapping nonlinear dynamics to a linear space using eigenfunctions. Unfortunately, finding such…

Dynamic Mode Decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman…

The goals and contributions of this paper are twofold. It provides a new computational tool for data driven Koopman spectral analysis by taking up the formidable challenge to develop a numerically robust algorithm by following the natural…

Kohn-Sham density functional theory is the base of modern computational approaches to electronic structures. Their accuracy vitally relies on the exchange-correlation energy functional, which encapsulates electron-electron interaction…

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…