Low-variance estimators for nuclear quantum mean forces
Abstract
Quantum nuclear effects on the statistical properties of position-dependent operators can be rigorously captured by molecular dynamics on the learnt potential of mean force of a single path-integral replica. However, the primitive mean-force averages obtained from path integral molecular dynamics with that replica held fixed are noisy. We derive a "scaled gradient" estimator with zero variance for a one-dimensional harmonic oscillator. On our molecular benchmark systems, the Zundel cation at 100 K and 300 K and bulk water at 300 K we observe nearly 5 to 50 times reduction in sampling time. The resulting potentials can be trained on these forces like standard machine learning interatomic potentials and yield stable production simulations from which quantum expectation values of position-dependent observables are obtained as classical ensemble averages.
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BibTeX
@misc{kapil2026lowvariance,
title = {{Low-variance estimators for nuclear quantum mean forces}},
author = {Venkat Kapil},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32652},
eprint = {2610.32652},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32652},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Low-variance estimators for nuclear quantum mean forces
AU - Venkat Kapil
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.32652
UR - https://arxiv.org/abs/2610.32652
AB - Quantum nuclear effects on the statistical properties of position-dependent operators can be rigorously captured by molecular dynamics on the learnt potential of mean force of a single path-integral replica. However, the primitive mean-force averages obtained from path integral molecular dynamics with that replica held fixed are noisy. We derive a "scaled gradient" estimator with zero variance for a one-dimensional harmonic oscillator. On our molecular benchmark systems, the Zundel cation at 100 K and 300 K and bulk water at 300 K we observe nearly 5 to 50 times reduction in sampling time. The resulting potentials can be trained on these forces like standard machine learning interatomic potentials and yield stable production simulations from which quantum expectation values of position-dependent observables are obtained as classical ensemble averages.
ER -