Studying inhomogeneous quantum many-body problems using neural networks

We show how convolutional neural networks can be employed to learn the mapping from arbitrary potential landscapes to observables in quantum many-body systems. While following the general spirit of density-functional theory, our approach can easily be applied without modification to a wide variety of settings, effectively learning the significant underlying physical principles from raw training data. We verify the performance of this framework for a number of examples such as the prediction of Friedel oscillations and level spacing statistics. Our network architecture allows us to predict on system sizes larger than seen in the training data, and we analyze its scaling performance