Fast evaluation of interaction integrals for confined systems with machine learning

TL;DR

This paper introduces a neural network-based method to efficiently compute interaction integrals in confined quantum systems, significantly reducing computational costs while maintaining controllable accuracy.

Contribution

The novel use of a shallow neural network for fast and accurate evaluation of two-electron integrals in confined systems is presented.

Findings

Speed-up in energy level calculations

Controllable accuracy in integral evaluation

Applicable to general isotropic interaction potentials

Abstract

The calculation of interaction integrals is a bottleneck for the treatment of many-body quantum systems due to its high numerical cost. We conduct configuration interaction calculations of the few-electron states confined in III-V semiconductor 2D structures using a shallow neural network to calculate the two-electron integrals, that can be used for general isotropic interaction potentials. This approach allows for a speed up of the evaluation of the energy levels and a controllable accuracy.