Building Accurate Exchange-Correlation Functional for Density Functional Theory Through Data Analytics and Optimization

Density functional theory (DFT) forms the foundation for computing the electronic structure of many-electron systems through the Kohn-Sham (KS) equations, with electron density <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>(<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i>) serving as the fundamental variable. This approach allows for the understanding and manipulation of material properties at the atomic and electronic levels. However, the exchange-correlation (XC) functional in DFT is not known in an exact form and is typically approximated using analytical models, which limits the accuracy of DFT calculations. The recent advancements in data analytics techniques, such as machine learning, which excel in pattern recognition, offer new opportunities for more effective approximations of the XC functional. In this study, we introduce a novel approach for XC functional modeling by fusing shared representation learning. This method leverages information sharing across tasks to improve the fused XC (FXC) functional model generalization. To improve the robustness of the FXC functional model, we further develop a multi-objective constrained multitask adjustment mechanism. Additionally, to expedite the determination of the optimal FXC model, we propose a group-theory-based multi-objective optimization (MOO) algorithm, which enables faster exploration of the solution space. Our experimental results demonstrate that the KS equations incorporating the FXC functional substantially improve the accuracy of molecular atomization energies, ionization potentials, and electron density calculations. Moreover, the method exhibits applicability to the computation of isomerization reaction energies in large molecules. These findings validate the effectiveness of our data analytics and optimization-based approach in enhancing the precision of the XC functional approximation.