Machine learning quantum mechanics: solving quantum mechanics problems using radial basis function networks

TL;DR

This paper demonstrates that machine learning, specifically radial basis function networks, can effectively solve quantum mechanics problems by approximating ground states and eigenvalues with good accuracy.

Contribution

It introduces the use of radial basis function networks as variational wavefunctions in quantum mechanics, applying variational Monte Carlo methods to solve simple Hamiltonians.

Findings

Good agreement with theoretical values for ground states

Successful calculation of smallest eigenvalues of Hermitian matrices

Machine learning techniques can solve quantum problems effectively

Abstract

Inspired by the recent work of Carleo and Troyer[1], we apply machine learning methods to quantum mechanics in this article. The radial basis function network in a discrete basis is used as the variational wavefunction for the ground state of a quantum system. Variational Monte Carlo(VMC) calculations are carried out for some simple Hamiltonians. The results are in good agreements with theoretical values. The smallest eigenvalue of a Hermitian matrix can also be acquired using VMC calculations. Our results demonstrate that machine learning techniques are capable of solving quantum mechanical problems.