Machine Learning the Physical Non-Local Exchange-Correlation Functional of Density-Functional Theory

Understand

We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and potential.

• This functional is extremely non-local, but retains the computational scaling of traditional local or semi-local approximations.
• It therefore holds the promise of solving some of the delocalization problems that plague density-functional theory, while maintaining the computational efficiency that characterizes the Kohn-Sham equations.
• Furthermore, by using automatic differentiation, a capability present in modern machine-learning frameworks, we impose the exact mathematical relation between the exchange-correlation energy and the potential, leading to a fully consistent method.