Emulators for scarce and noisy data: application to auxiliary field diffusion Monte Carlo for the deuteron

TL;DR

This paper develops and compares three emulators for auxiliary field diffusion Monte Carlo (AFDMC) applied to the deuteron, demonstrating that the parametric matrix model significantly outperforms others in accuracy and speed, even with limited training data.

Contribution

Introduces a reduced-basis emulator and compares it with a parametric matrix model and Gaussian Process emulator for AFDMC, highlighting the superior performance of the PMM.

Findings

PMM achieves ~0.1% error and 10^7 speed-up

All emulators validated against ~1000 exact solutions

PMM outperforms RBM and Gaussian Process emulators

Abstract

The validation, verification, and uncertainty quantification of computationally expensive theoretical models of quantum many-body systems require the construction of fast and accurate emulators. In this work, we develop emulators for auxiliary field diffusion Monte Carlo (AFDMC), a powerful many-body method for nuclear systems. We introduce a reduced-basis method (RBM) emulator for AFDMC and study it in the simple case of the deuteron. Furthermore, we compare our RBM emulator with the recently proposed parametric matrix model (PMM) that combines elements of RBMs with machine learning. We contrast these two approaches with a traditional Gaussian Process emulator. All three emulators constructed here are based on a very limited set of 5 training points, as expected for realistic AFDMC calculations, but validated against $\mathcal{O}(10^3)$ exact solutions. We find that the PMM, with emulator errors of only $\approx 0.1 \%$ and speed-up factors of $\approx 10^7$, outperforms our implementation of the other two emulators when applied to AFDMC.