An efficient sampling algorithm for Variational Monte Carlo

TL;DR

This paper introduces a new sampling algorithm for Variational Monte Carlo that improves efficiency by combining a modified Langevin dynamics discretization with a Metropolis step, outperforming traditional importance sampling methods.

Contribution

The paper presents a novel sampling algorithm for VMC based on a modified Ricci-Ciccotti discretization with Metropolis correction, enhancing sampling efficiency.

Findings

Algorithm outperforms standard importance sampling in numerical tests.

Effective for atomic and molecular systems like Lithium, Fluorine, Copper, and phenol.

Demonstrates improved sampling accuracy and convergence.

Abstract

We propose a new algorithm for sampling the $N$-body density $|\Psi({\bf R})|^2/\int_{\mathbb{R}^{3N}} |\Psi|^2$ in the Variational Monte Carlo (VMC) framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space $({\bf R},{\bf P})$ improved by a Metropolis acceptation/rejection step. We show through some representative numerical examples (Lithium, Fluorine and Copper atoms, and phenol molecule), that this algorithm is superior to the standard sampling algorithm based on the biased random walk (importance sampling).