Teaching a Neural Network Quantum Mechanics. A Deep Learning Approach to the N-Representability Problem.

Abstract: We show that an unsupervised artificial neural network can be trained to parameterize the set of N representable density matrices well enough to enable ground state energy calculations. A one-dimensional harmonic oscillator system is used to test the method. 4, 5, or 6 fermions are placed in an external potential. They interact with one of three different interaction types. By choosing the most successful network according to a well-defined measure, the approach is shown to generalize to interaction types not considered by the measure.