Deep learning and the Schr\"odinger equation

TL;DR

This paper demonstrates that deep convolutional neural networks can accurately predict the ground-state energy and other properties of electrons in complex two-dimensional potentials, achieving chemical accuracy without explicit analytical solutions.

Contribution

The study introduces a neural network approach to estimate quantum energies in arbitrary potentials, outperforming traditional methods in accuracy and speed.

Findings

Median absolute error of 1.49 mHa in energy prediction

Effective prediction of kinetic and excited-state energies

Neural network generalizes well to unseen potentials

Abstract

We have trained a deep (convolutional) neural network to predict the ground-state energy of an electron in four classes of confining two-dimensional electrostatic potentials. On randomly generated potentials, for which there is no analytic form for either the potential or the ground-state energy, the neural network model was able to predict the ground-state energy to within chemical accuracy, with a median absolute error of 1.49 mHa. We also investigate the performance of the model in predicting other quantities such as the kinetic energy and the first excited-state energy of random potentials.