Bridging electronic and classical density-functional theory using universal machine-learned functional approximations
Abstract
The accuracy of density-functional theory (DFT) is determined by the quality of the approximate functionals, such as exchange-correlation in electronic DFT and the excess functional in the classical DFT formalism of fluids. The exact functional is highly nonlocal for both electrons and fluids, yet most approximate functionals are semi-local or nonlocal in a limited weighted-density form. Machine-learned (ML) nonlocal density-functional approximations are promising in both electronic and classical DFT, but have so far employed disparate approaches with limited generality. Here, we formulate a universal approximation framework and training protocol for nonlocal ML functionals, combining features of equivariant convolutional neural networks and the weighted-density approximation. We prototype this approach for several 1D and quasi-1D problems and demonstrate that a functional with exactly the same hyperparameters achieves excellent accuracy for the hard-rod fluid, the inhomogeneous Ising model, the exact exchange functional for electrons, the electron kinetic energy functional for orbital-free DFT, as well as for liquid water with 1D inhomogeneities. These results lay the foundation for a universal ML approach to exact 3D functionals spanning electronic and classical DFT.
AI-Generated Overview
-
Research Focus: The study aims to bridge the gap between electronic density-functional theory (DFT) and classical DFT using a universal machine-learned framework to develop nonlocal functional approximations applicable to both realms.
-
Methodology: A universal machine learning (ML) framework integrating equivariant convolutional neural networks and the weighted-density approximation is devised. This framework is trained on various problems, including hard-rod fluids, the inhomogeneous Ising model, electronic exchange energy, and liquid water, using a consistent set of hyperparameters.
-
Results: The ML approach achieved excellent accuracy across diverse systems by employing the same hyperparameters, demonstrating commendable performance in representing complex nonlocal functional dependencies, including those of classical fluids and electronic structures.
-
Key Contribution(s): The paper presents a novel universal ML framework for nonlocal functionals that performs equally well for both quantum and classical systems, showcasing the capability to address the limitations of conventional approximations in DFT.
-
Significance: This work highlights the potential of ML techniques to enhance the accuracy of density-functional approximations significantly, particularly in contexts where classical DFT has struggled, thereby broadening the applicability of DFT across various scientific disciplines.
-
Broader Applications: The universal ML functional can be used in various fields such as materials science, chemistry, and physics, potentially streamlining the computational processes in modeling complex systems, including solvent-solute interactions and improving classical DFT applications through more accurate functional approximations.