A light weight regularization for wave function parameter gradients in quantum Monte Carlo

Pathak, Shivesh; Wagner, Lucas K.

doi:10.1063/5.0004008

A light weight regularization for wave function parameter gradients in quantum Monte Carlo

Journal Article · Thu Aug 06 00:00:00 EDT 2020 · AIP Advances

DOI:https://doi.org/10.1063/5.0004008· OSTI ID:1659258

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Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics; University of Illinois at Urbana-Champaign
Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics

The parameter derivative of the expectation value of the energy, ∂E/∂p, is a key ingredient in variational Monte Carlo (VMC) wave function optimization methods. In some cases, a naïve estimate of this derivative suffers from an infinite variance, which inhibits the efficiency of optimization methods that rely on a stable estimate of the derivative. In this work, we derive a simple regularization of the naïve estimator, which is trivial to implement in existing VMC codes, has finite variance, and a negligible bias, which can be extrapolated to zero bias with no extra cost. We use this estimator to construct an unbiased, finite variance estimation of ∂E/∂p for a multi-Slater–Jastrow trial wave function on the LiH molecule and in the optimization of a multi-Slater–Jastrow trial wave function on the CuO molecule. This regularized estimator is a simple and efficient estimator of ∂E/∂p for VMC optimization techniques.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: AC05-00OR22725; SC0020177

OSTI ID:: 1659258

Alternate ID(s):: OSTI ID: 1646530

Journal Information:: AIP Advances, Journal Name: AIP Advances Journal Issue: 8 Vol. 10; ISSN 2158-3226

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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A light weight regularization for wave function parameter gradients in quantum Monte Carlo

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