A light weight regularization for wave function parameter gradients in quantum Monte Carlo
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 01, 2020
- Source ID
- 10.1063/5.0004008
Entities
People
- Lucas K Wagner
- Shivesh Pathak
Organizations
- National Geospatial-Intelligence Agency
- National Science Foundation
- United States Department of Energy
- University of Illinois Urbana–Champaign