Accurate and Efficient Emulation of Proton-Deuteron Scattering via the Reduced Basis Method and Active Learning

TL;DR

This paper presents highly accurate and efficient emulators for proton-deuteron scattering calculations, utilizing reduced basis methods and active learning to enable fast, precise predictions for nuclear physics applications.

Contribution

The authors develop novel reduced basis emulators for proton-deuteron scattering, achieving unprecedented accuracy with minimal training data and enabling rapid exploration of parameter space.

Findings

Emulators achieve relative errors as low as 10^{-7}.

Significant acceleration in scattering prediction exploration.

Applicable for calibrating three-nucleon forces and uncertainty quantification.

Abstract

We introduce highly accurate and efficient emulators for proton-deuteron scattering below the deuteron breakup threshold. We explore two different reduced-basis method strategies: one based on the Kohn variational principle and another on Galerkin projections of the underlying system of linear equations. We use the adaptive greedy algorithm previously developed for two-body scattering for optimal selection of high-fidelity training points in the input parameter space. We demonstrate that these emulators reproduce ab initio hyperspherical harmonics calculations of $R$-matrix elements with remarkable precision, achieving relative errors as low as $10^{-7}$ with a small number of training points, even in regions of strong nonlinear parameter dependence. They also dramatically accelerate the exploration of the scattering predictions in the parameter space, a capability highly desired for calibrating (chiral) three-nucleon forces against scattering measurements. Our formalism can be further generalized to handle nucleon-deuteron scattering above the breakup threshold. These emulator developments will provide valuable tools to accelerate uncertainty quantification and rigorous parameter inference in the study of nuclear forces.