High-Dimensional Operator Learning for Molecular Density Functional Theory

TL;DR

This paper introduces an optimized neural operator learning approach that simplifies high-dimensional molecular density profiles into lower-dimensional components, enabling accurate and efficient classical density functional theory calculations for complex chemical systems.

Contribution

The work presents a novel neural operator model that effectively reduces dimensionality in cDFT, improving accuracy and computational efficiency for molecular density predictions.

Findings

Accurately maps density profiles to direct correlation functions.

Reduces computational complexity exponentially.

Generalizes to complex molecular systems.

Abstract

Classical density functional theory (cDFT) provides a systematic approach to predict the structure and thermodynamic properties of chemical systems through the single-molecule density profiles. Whereas the statistical-mechanical framework is theoretically rigorous, its practical applications are often constrained by challenges in formulating a reliable free-energy functional and the complexity of solving multidimensional integro-differential equations. In this work, we established an optimized operator learning method that effectively separates the high-dimensional molecular density profile into two lower-dimensional components, thereby exponentially reducing the vast input space. The convoluted operator learning network demonstrates exceptional learning capabilities, accurately mapping the relationship between the density profile of a carbon dioxide system to its one-body direct correlation function using an atomistic polarizable model. The neural operator model can be generalized to more complex systems, offering high-precision cDFT calculations at low computational cost.