Simple and Effective: Machine Learning-Driven Nonlocal Functionals for Orbital-Free DFT

Orbital-Free DFT holds the promise to predict the electronic structure at any temperature of mesoscopic, realistically sized systems merely requiring a computational cost that grows linearly with system size. The most accurate functionals of the kinetic energy are nonlocal with a density-dependent kernel. Unfortunately, their use is hampered by the computational complexity intrinsic in the evaluation of the kernel. In this talk, we present a useful, yet simple extension of computationally cheap nonlocal kinetic energy functionals with density-independent kernel whose kernel is evaluated by a machine learning algorithm. The resulting, ML-aided functionals show much improved applicability compared to their non-ML-aided ancestors. For example, the well-known limitation of the Wang-Teter functional in its ability to model phases of bulk Si is completely cured by its ML-aided extension employing Gaussian Process Regression. We discuss several routes for training the models involved and critically assess their performance.

References:

Shao, X., Mi, W., & Pavanello, M. (2021). Revised Huang-Carter nonlocal kinetic energy functional for semiconductors and their surfaces. Physical Review B, 104(4), 045118.

Wenhui Mi, Alessandro Genova, Michele Pavanello; Nonlocal kinetic energy functionals by functional integration. J. Chem. Phys. 14 May 2018; 148 (18): 184107.

Wang, Y. A., Govind, N., & Carter, E. A. (1999). Orbital-free kinetic-energy density functionals with a density-dependent kernel. Physical Review B, 60(24), 16350.