Speaker
Description
Machine-learned regression models represent a promising tool to implement accurate and compu-
tationally affordable energy-density functionals to solve quantum many-body problems via density
functional theory. However, in continuous systems, while they can easily be trained to accurately map ground-state density
profiles to the corresponding energies, their functional derivatives often turn out to be too noisy,
leading to instabilities in self-consistent iterations and in gradient-based searches of the ground-state
density profile. We investigate how these instabilities occur when standard deep neural networks
are adopted as regression models, and we show how to avoid them using an ad-hoc convolutional archi-
tecture featuring an inter-channel averaging layer.
Furthermore we study how this methods can be extended to spin models relevant for quantum simulators, considering a 1d quantum transverse
Ising model with nearest-neighbours interaction. We study the conditions for applying DFT in quantum discrete systems and we implement a different kind of
architecture (U-NET) to map the magnetization per site to the functional per site.
noninteracting atoms in optical speckle disorder. With the inter-channel average, accurate and sys-
tematically improvable ground-state energies and density profiles are obtained via gradient-descent
optimization, without instabilities nor violations of the variational principle.
