High-Dimensional Operator Learning for Molecular Density Functional Theory

Classical density functional theory (cDFT) provides a systematic framework to predict the structure and thermodynamic properties of chemical systems through molecular density profiles. Whereas the statistical-mechanical framework is theoretically rigorous, its 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 a convolutional operator learning method that effectively separates the high-dimensional molecular density profile into lower-dimensional components, thereby exponentially reducing the vast input space. The operator learning network demonstrates exceptional learning capabilities, accurately mapping the relationship between the molecular density profile and its one-body direct correlation function for an atomistic polarizable model of carbon dioxide. The machine-learning procedure can be generalized to more complex molecular systems, offering high-precision operator-cDFT calculations at a low computational cost.