Learning the exchange-correlation functional from nature with fully differentiable density functional theory

Improving the predictive capability of molecular properties in {\it ab initio} simulations is essential for advanced material discovery. Despite recent progress making use of machine learning, utilizing deep neural networks to improve quantum chemistry modelling remains severely limited by the scarcity and heterogeneity of appropriate experimental data. Here we show how training a neural network to replace the exchange-correlation functional within a fully-differentiable three-dimensional Kohn-Sham density functional theory (DFT) framework can greatly improve simulation accuracy. Using only eight experimental data points on diatomic molecules, our trained exchange-correlation network provided improved prediction of atomization and ionization energies across a collection of 110 molecules when compared with both commonly used DFT functionals and more expensive coupled cluster simulations.