Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors

In this work, the authors explore a framework for developing machine-learned exchange-correlation (XC) functionals. The approach consists of two parts: a rotationally invariant model space constructed from convolutional kernels, and a neural network to predict the XC energy density. The results show that increasing the number of features in the model space leads to systematically improvable approximations to the B3LYP XC energy for 21 small molecule systems. The XC formation energy is predicted to chemical accuracy based on orbital free descriptors with a range of $<$0.2 Angstrom, suggesting this approach provides an efficient route toward semi-local approximations of hybrid functionals.