Variance reduction for forces and pressure in variational Monte Carlo

Fuente: arXiv
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Main Authors: Linteau, David, Moroni, Saverio, Carleo, Giuseppe, Holzmann, Markus
Format: Preprint
Published: 2026
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author Linteau, David
Moroni, Saverio
Carleo, Giuseppe
Holzmann, Markus
author_facet Linteau, David
Moroni, Saverio
Carleo, Giuseppe
Holzmann, Markus
contents We present simple and practical strategies to reduce the variance of Monte Carlo estimators. Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying ideas apply more broadly to other observables, like pair-correlation and angular-distribution functions, and other methods, including molecular dynamics. For Pulay-type contributions, we show that a minor modification based on the Metropolis acceptance ratio softens the power-law divergence of the variance to a logarithmic one, and that inexpensive regularizations can further suppress outliers at the price of a controlled small bias. For Hellmann-Feynman forces, we derive compact variance-reduced estimators for periodic systems that are straightforward to implement in standard Monte Carlo codes. The approach is illustrated for high-pressure metallic hydrogen with more than a hundred atoms described by neural quantum states, including an application to molecular dynamics driven by the improved forces.
format Preprint
id arxiv_https___arxiv_org_abs_2603_14521
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Variance reduction for forces and pressure in variational Monte Carlo
Linteau, David
Moroni, Saverio
Carleo, Giuseppe
Holzmann, Markus
Strongly Correlated Electrons
Quantum Physics
We present simple and practical strategies to reduce the variance of Monte Carlo estimators. Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying ideas apply more broadly to other observables, like pair-correlation and angular-distribution functions, and other methods, including molecular dynamics. For Pulay-type contributions, we show that a minor modification based on the Metropolis acceptance ratio softens the power-law divergence of the variance to a logarithmic one, and that inexpensive regularizations can further suppress outliers at the price of a controlled small bias. For Hellmann-Feynman forces, we derive compact variance-reduced estimators for periodic systems that are straightforward to implement in standard Monte Carlo codes. The approach is illustrated for high-pressure metallic hydrogen with more than a hundred atoms described by neural quantum states, including an application to molecular dynamics driven by the improved forces.
title Variance reduction for forces and pressure in variational Monte Carlo
topic Strongly Correlated Electrons
Quantum Physics
url https://arxiv.org/abs/2603.14521