The Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks

TL;DR

This paper introduces a convolutional neural network that predicts the kinetic energy of hydrocarbons from electron density, serving as a non-local correction to improve traditional kinetic functionals in density functional theory.

Contribution

The study presents a neural network-based approach to accurately approximate Kohn-Sham kinetic energy, enhancing the modeling of potential energy surfaces in hydrocarbons.

Findings

Qualitative reproduction of Kohn-Sham potential energy surfaces

Identification of numerical noise as a key challenge

Analysis of learned density features for model generalization

Abstract

We demonstrate a convolutional neural network trained to reproduce the Kohn-Sham kinetic energy of hydrocarbons from electron density. The output of the network is used as a non-local correction to the conventional local and semi-local kinetic functionals. We show that this approximation qualitatively reproduces Kohn-Sham potential energy surfaces when used with conventional exchange correlation functionals. Numerical noise inherited from the non-linearity of the neural network is identified as the major challenge for the model. Finally we examine the features in the density learned by the neural network to anticipate the prospects of generalizing these models.