Related papers: Energy derivatives in real-space diffusion Monte C…
We present quantum Monte Carlo calculations of total energy derivatives, consistently performed in the fixed-node approximation. Contributions from nodal displacements, neglected or approximated in previous investigations, are properly…
The optimization of neural wave functions in variational Monte Carlo crucially relies on a robust convergence criterion. While the energy variance is theoretically a definitive measure, its practical application as a primary convergence…
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a {\bf fixed}…
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. The remaining…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
The parameter derivative of the expectation value of the energy, $\partial E/\partial p$, is a key ingredient in variational quantum Monte Carlo (VMC) wave function optimization methods. In some cases, a na\"ive Monte Carlo estimate of this…
This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on…
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The…
The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time discretized diffusion process. We present a robust and practical method to determine the effective…
We investigate how the fixed-node diffusion Monte Carlo energy of solids depends on single-particle orbitals used in Slater--Jastrow wave functions. We demonstrate that the dependence can be significant, in particular in the case of 3d…
The energy variance optimization algorithm over a fixed ensemble of configurations in variational Monte Carlo is formally identical to a problem of fitting data: we reexamine it from a statistical maximum-likelihood point of view. We detect…
Direct sampling of multi-dimensional systems with quantum Monte Carlo methods allows exact account of many-body effects or particle correlations. The most straightforward approach to solve the Schr\"odinger equation, Diffusion Monte Carlo,…
In the regime where traditional approaches to electronic structure cannot afford to achieve accurate energy differences via exhaustive wave function flexibility, rigorous approaches to balancing different states' accuracies become…
A diffusion Monte Carlo algorithm is introduced that can determine the correct nodal structure of the wave function of a few-fermion system and its ground-state energy without an uncontrolled bias. This is achieved by confining signed…
Fixed-node diffusion Monte Carlo (DMC) is a stochastic algorithm for finding the lowest energy many-fermion wave function with the same nodal surface as a chosen trial function. It has proved itself among the most accurate methods available…
We present a method for optimizing the location of the fermion ground-state nodes using a combination of diffusion Monte Carlo (DMC) and projected gradient descent (PGD). A PGD iteration shifts the parameters of an arbitrary node-fixing…
We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…