Efficient Solutions of Fermionic Systems using Artificial Neural Networks

TL;DR

This paper explores the use of shallow neural networks, specifically restricted Boltzmann machines, to efficiently model fermionic systems in quantum physics, demonstrating scalability to large electron numbers and implementation on high-performance computing systems.

Contribution

It introduces neural-network-based wave functions for fermionic systems, compares them with traditional methods, and discusses efficient implementation on advanced computing architectures.

Findings

Neural network wave functions can model complex fermionic correlations.

The methods scale to systems with up to 90 electrons.

Efficient implementation on high-performance computing systems is feasible.

Abstract

We discuss differences and similarities between variational Monte Carlo approaches that use conventional and artificial neural network parameterizations of the ground-state wave function for systems of fermions. We focus on a relatively shallow neural-network architectures, the so called restricted Boltzmann machine, and discuss unsupervised learning algorithms that are suitable to model complicated many-body correlations. We analyze the strengths and weaknesses of conventional and neural-network wave functions by solving various circular quantum-dots systems. Results for up to 90 electrons are presented and particular emphasis is placed on how to efficiently implement these methods on homogeneous and heterogeneous high-performance computing facilities.