Neural Density Functional Theory in Higher Dimensions with Convolutional Layers

TL;DR

This paper introduces a convolutional neural network model for 2D density functional theory applied to hard disks, demonstrating accurate predictions and potential extension to 3D systems.

Contribution

It develops a convolutional layer-based machine learning model for 2D density functional theory, extending previous 1D approaches and showing promising results for inhomogeneous systems.

Findings

Model achieves good agreement with simulations for pair correlation functions.

The approach is applicable to 3D problems with suitable training data.

Uses only convolutional layers for efficient computation.

Abstract

Based on recent advancements in using machine learning for classical density functional theory for systems with one-dimensional, planar inhomogeneities, we propose a machine learning model for application in two dimensions (2D) akin to density functionals in weighted density forms, as e. g. in fundamental measure theory (FMT). We implement the model with fast convolutional layers only and apply it to a system of hard disks in fully 2D inhomogeneous situations. The model is trained on a combination of smooth and steplike external potentials in the fluid phase. Pair correlation functions from test particle geometry show very satisfactory agreement with simulations although these types of external potentials have not been included in the training. The method should be fully applicable to 3D problems, where the bottleneck at the moment appears to be in obtaining smooth enough 3D histograms as training data from simulations.