Related papers: Accelerated density matrix expansions for Born-Opp…
Density matrices evolved according the von Neumann equation are commonly used to simulate the dynamics of driven quantum systems. However, computational methods using density matrices are often too slow to explore the large parameter spaces…
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients…
We present an efficient general approach to first principles molecular dynamics simulations based on extended Lagrangian Born-Oppenheimer molecular dynamics in the limit of vanishing self-consistent field optimization. The reduction of the…
A Lagrangian generalization of time-reversible Born-Oppenheimer molecular dynamics [Niklasson et al., Phys. Rev. Lett. vol. 97, 123001 (2006)] is proposed. The Lagrangian includes extended electronic degrees of freedom as auxiliary…
The recent progress of linear-scaling or O(N) methods in the density functional theory (DFT) is remarkable. We expect that first-principles molecular dynamics (FPMD) simulations based on DFT can now treat more realistic and complex systems…
Extended Lagrangian Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
To leverage the redundancy between the electronic structure computed at each step of first-principles molecular dynamics, we present a data-driven modeling framework for Kohn-Sham Density Functional Theory that bypasses the explicit…
Kohn-Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. We present…
A purification algorithm for expanding the single-particle density matrix in terms of the Hamiltonian operator is proposed. The scheme works with a predefined occupation and requires less than half the number of matrix-matrix…
The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
Despite its widespread use in materials science, conventional molecular dynamics (MD) simulations are severely constrained by timescale limitations. To address this shortcoming, we propose an empirical formulation of accelerated MD method,…
This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. In this paper, we…
In this paper, we consider the alleviation of the boundary problem when the probability density function has bounded support. We apply Robbins-Monro's algorithm and Bernstein polynomials to construct a recursive density estimator. We study…
Wavefunction extrapolation greatly reduces the number of self-consistent field (SCF) iterations and thus the overall computational cost of Born-Oppenheimer molecular dynamics (BOMD) that is based on the Kohn-Sham density functional theory.…
This paper presents an accelerated quadrature scheme for the evaluation of layer potentials in three dimensions. Our scheme combines a generic, high order quadrature method for singular kernels called Quadrature by Expansion (QBX) with a…
Geometry optimization is an important part of both computational materials and surface science because it is the path to finding ground state atomic structures and reaction pathways. These properties are used in the estimation of…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…