Machine-learning approach to finite-size effects in systems with strongly interacting fermions

TL;DR

This paper explores how machine learning, especially neural networks, can effectively extrapolate finite-size many-body physics calculations to the thermodynamic limit, addressing challenges like small datasets and discontinuities.

Contribution

It introduces a systematic approach using neural networks to improve finite-size extrapolations in many-body systems, including neutron matter and the unitary gas.

Findings

Neural networks successfully extrapolate to the thermodynamic limit.

New metrics help avoid spurious effects in machine learning models.

Auxiliary Field Diffusion Monte Carlo calculations support the study.

Abstract

We investigate the applicability of machine learning techniques in studying the finite-size effects associated with many-body physics. These techniques have an emerging presence in many-body theory as they have been used for interpolations, extrapolations, and in modeling wavefunctions. We will resolve several issues associated with machine learning and many-body calculations such as small datasets, outliers, and discontinuities, for the purpose of extrapolating finite calculations to macroscopic scales. We carry out a systematic investigation of two related systems by developing metrics that aim to avoid spurious effects and capture desired features. This work uses neural networks to extrapolate the Unitary Gas to the thermodynamic limit at zero-range, which is otherwise difficult to reach. The effective mass of strongly interacting neutron matter is also studied and makes use of the non-interacting problem to resolve discontinuous predictions. For this investigation, we also carried out new Auxiliary Field Diffusion Monte Carlo (AFDMC) calculations for a variety of densities and particle numbers. Ultimately, we demonstrate an effective utility for neural networks in this context.