Back to Search Start Over

Rayleigh-Gauss-Newton optimization with enhanced sampling for variational Monte Carlo

Authors :
Robert J. Webber
Michael Lindsey
Source :
Physical Review Research, Vol 4, Iss 3, p 033099 (2022)
Publication Year :
2022
Publisher :
American Physical Society, 2022.

Abstract

Variational Monte Carlo (VMC) is an approach for computing ground-state wave functions that has recently become more powerful due to the introduction of neural network-based wave-function parametrizations. However, efficiently training neural wave functions to converge to an energy minimum remains a difficult problem. In this work, we analyze optimization and sampling methods used in VMC and introduce alterations to improve their performance. First, based on theoretical convergence analysis in a noiseless setting, we motivate a new optimizer that we call the Rayleigh-Gauss-Newton method, which can improve upon gradient descent and natural gradient descent to achieve superlinear convergence at no more than twice the computational cost. Second, to realize this favorable comparison in the presence of stochastic noise, we analyze the effect of sampling error on VMC parameter updates and experimentally demonstrate that it can be reduced by the parallel tempering method. In particular, we demonstrate that RGN can be made robust to energy spikes that occur when the sampler moves between metastable regions of configuration space. Finally, putting theory into practice, we apply our enhanced optimization and sampling methods to the transverse-field Ising and XXZ models on large lattices, yielding ground-state energy estimates with remarkably high accuracy after just 200 parameter updates.

Subjects

Subjects :
Physics
QC1-999

Details

Language :
English
ISSN :
26431564
Volume :
4
Issue :
3
Database :
Directory of Open Access Journals
Journal :
Physical Review Research
Publication Type :
Academic Journal
Accession number :
edsdoj.4a84129b4a3545a2b00b43cb1f370edc
Document Type :
article
Full Text :
https://doi.org/10.1103/PhysRevResearch.4.033099