Essential difference between the machine learning and artificial Kohn-Sham potentials

The Kohn-Sham density functional theory is widely used to predict physical or chemical properties of various materials with its practical accuracy and computational cost. Its accuracy depends on the exchange-correlation functional. Although there exist many approximations for the functional, its entire structure is yet elusive since the reference databases and physical conditions available are limited. On the other hand, we develop another strategy; the functional structure is represented with a flexible neural network and its parameters are trained with machine-learning algorithms[1]. The NN-based functional becomes transferable enough by training with the density, which contains abundant information in the 3D space.

Here, we analyze the properties of the machine-learning density functionals. We investigate essential differences between the machine-learned functionals and artificial functionals by comparing their performance using accurate densities and ones from artificial functionals as the training data.


[1] R. Nagai, R. Akashi, and O. Sugino, arXiv:1903.00238 (2019).
[2] R. Nagai, K. Burke, R. Akashi, and O. Sugino, in preparation.