Constrained Machine Learning de-orbitalization of meta-GGA exchange-correlation functionals

Meta-generalized-gradient-approximation (mGGA) exchange-correlation functionals commonly take the orbital kinetic energy density τ(r) as an ingredient in their construction [1]. Such τ(r) dependent functionals have shown impressive performance for diverse problems, but orbital dependence of τ(r) complicates the exchange-correlation potential and increases computational cost. Recently, Rodriguez et.al. constructed a mGGA with laplacian▽²n without significantly degrading accuracy [2]. This suggests an intriguing but unclear relationship between τ(r) and ▽²n . We exploit this relationship using machine learning combined with exact constraints to explore how neural-network models can de-orbitalize functionals and model fundamental components of Kohn-Sham density functional theory.

[1] Jianwei Sun et.al. Phys. Rev. Lett. 115,036402 (2015)
[2] Mejia-Rodriguez et.al. Phys. Rev. A 96, 052512 (2017)