High-Dimensional Operator Learning for Molecular Density Functional Theory.

Area of Science:

• Computational chemistry
• Statistical mechanics
• Machine learning

Background:

• Classical density functional theory (cDFT) offers a rigorous framework for predicting chemical system properties using molecular density profiles.
• Practical applications of cDFT are hindered by difficulties in developing accurate free-energy functionals and solving complex multidimensional equations.

Purpose of the Study:

• To develop a novel convolutional operator learning method to overcome the computational challenges in classical density functional theory.
• To significantly reduce the input space complexity for density profile analysis.

Main Methods:

• A convolutional operator learning network was established to decompose high-dimensional molecular density profiles into lower-dimensional components.
• The network was trained to map molecular density profiles to their corresponding one-body direct correlation functions.
• The method was applied to an atomistic polarizable model of carbon dioxide.

Main Results:

• The operator learning network demonstrated high accuracy in mapping density profiles to correlation functions.
• The method successfully reduced the computational complexity associated with cDFT calculations.
• The approach showed potential for generalization to more complex molecular systems.

Conclusions:

• The developed convolutional operator learning method offers a computationally efficient and accurate approach for operator-cDFT calculations.
• This machine learning strategy significantly lowers the cost of high-precision calculations for chemical systems.
• The method holds promise for broader applications in computational chemistry and materials science.