Machine learned exchange and correlation functionals in density functional theory: progress and applications*

The fundamental theorems of density functional theory ensure that there exists an exact functional which provides the exact energy of a system from its exact density. This functional is minimized at a fixed electron number and a fixed external potential by the exact electron density, hence providing both the density and and energy.
It is, however, possible to approximate the exact functional, providing a balance between accuracy and computational cost.
In Kohn-Sham DFT, this balance depends on the choice of exchange and correlation functional, which only exists
in approximate form. Increasing the non-locality of this functional and climbing the figurative Jacob's ladder of DFT, one can systematically reduce the amount of approximation involved and thus approach the exact functional.
In this talk I will review our framework to create density functionals by using supervised machine learning. These functionals learn a meaningful representation of the physical information contained in the training data. I will show that these machine-learned functionals can be designed to lift the accuracy of local and semilocal functionals to that provided by more accurate methods while maintaining their baseline efficiency. In the second part of the talk I will address how machine learning methods can help to understand what
properties and conditions must the approximate Kohn-Sham exchange and correlation potential satisfy in order to obtain not only the exact energy but also the exact electronic density distribution.
Applications of these functionals to real and model systems will be presented.