Variance extrapolation method for neural-network variational Monte Carlo

TL;DR

This paper introduces a variance extrapolation method in neural-network variational Monte Carlo that accelerates convergence, improves energy estimates beyond ansatz limitations, and enhances error cancellation for better relative energy calculations.

Contribution

It proposes using training data for variance extrapolation in neural-network VMC, leading to faster convergence and more accurate energy estimations beyond traditional ansatz constraints.

Findings

Speeds up convergence of neural-network VMC

Surpasses ansatz limitations for energy estimation

Improves relative energy accuracy through error cancellation

Abstract

Constructing more expressive ansatz has been a primary focus for quantum Monte Carlo, aimed at more accurate \textit{ab initio} calculations. However, with more powerful ansatz, e.g. various recent developed models based on neural-network architectures, the training becomes more difficult and expensive, which may have a counterproductive effect on the accuracy of calculation. In this work, we propose to make use of the training data to perform variance extrapolation when using neural-network ansatz in variational Monte Carlo. We show that this approach can speed up the convergence and surpass the ansatz limitation to obtain an improved estimation of the energy. Moreover, variance extrapolation greatly enhances the error cancellation capability, resulting in significantly improved relative energy outcomes, which are the keys to chemistry and physics problems.