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

Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…

We introduce a new approach to density functional theory based on kinetic theory, showing that the Kohn-Sham equations can be derived as a macroscopic limit of a suitable Boltzmann kinetic equation in the limit of small mean free path…

The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical…

We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of…

Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…

We use projector operators to correct the Kohn-Sham Hamiltonian of density functional theory (KS-DFT) so that the resulting mean-field scheme yields, in finite systems, virtual orbitals and energy gaps in better agreement with those…

Soft robots are challenging to model and control as inherent non-linearities (e.g., elasticity and deformation), often requires complex explicit physics-based analytical modeling (e.g., a priori geometric definitions). While machine…

A remarkable consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of an injective map between the electronic density and any observable of the many electron problem in an external potential. In this work,…

We present recent developments of the NTChem program for performing large scale hybrid Density Functional Theory calculations on the supercomputer Fugaku. We combine these developments with our recently proposed Complexity Reduction…

This work presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to…

This paper derives rates of convergence of certain approximations of the Koopman operators that are associated with discrete, deterministic, continuous semiflows on a complete metric space $(X,d_X)$. Approximations are constructed in terms…

The mathematical properties and data-driven learning of the Koopman operator, which represents nonlinear dynamics as a linear mapping on a properly defined functional spaces, have become key problems in nonlinear system identification and…

Kernel analog forecasting (KAF), alternatively known as kernel principal component regression, is a kernel method used for nonparametric statistical forecasting of dynamically generated time series data. This paper synthesizes descriptions…

The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of classical mechanics. The main advantage…

Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of non-interacting particles, is the work horse of the theory. The particular form of…

We develop a stochastic formulation of the optimally-tuned range-separated hybrid density functional theory which enables significant reduction of the computational effort and scaling of the non-local exchange operator at the price of…

In this work we get insight into the impact of reduced density matrix functionals on the quality of removal/addition energies obtained using the Extended Koopmans' Theorem (EKT). Within reduced density matrix functional theory (RDMFT) the…

Probabilistic forecasting of complex phenomena is paramount to various scientific disciplines and applications. Despite the generality and importance of the problem, general mathematical techniques that allow for stable long-term forecasts…

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…

We present a substantial extension of our constraint-based approach for development of orbital-free (OF) kinetic-energy (KE) density functionals intended for the calculation of quantum-mechanical forces in multi-scale molecular dynamics…