Fast & accurate emulation of two-body scattering observables without wave functions

TL;DR

This paper introduces a rapid and precise emulator for two-body scattering observables that combines variational methods and eigenvector continuation, significantly reducing computational time while maintaining accuracy.

Contribution

The authors develop a novel emulator that efficiently approximates scattering observables using minimal exact solutions, enabling fast parameter studies and extrapolations.

Findings

Emulator accurately reproduces scattering observables with negligible error.

Achieves over 300x speedup in CPU time compared to exact calculations.

Effectively extrapolates beyond the training data range.

Abstract

We combine Newton's variational method with ideas from eigenvector continuation to construct a fast & accurate emulator for two-body scattering observables. The emulator will facilitate the application of rigorous statistical methods for interactions that depend smoothly on a set of free parameters. Our approach begins with a trial $K$ or $T$ matrix constructed from a small number of exact solutions to the Lippmann--Schwinger equation. Subsequent emulation only requires operations on small matrices. We provide several applications to short-range potentials with and without the Coulomb interaction and partial-wave coupling. It is shown that the emulator can accurately extrapolate far from the support of the training data. When used to emulate the neutron-proton cross section with a modern chiral interaction as a function of 26 free parameters, it reproduces the exact calculation with negligible error and provides an over 300x improvement in CPU time.