Abstract: In this talk, I will discuss how machine learning tools can be employed to solve the quantum many-fermion problem. I will specifically look at proof-of-principle simulations for the ground-state properties of fully polarized (or spinless), trapped, one-dimensional fermionic systems interacting through a gaussian potenial. I will discuss how to construct antisymmetric variational artificial neural network ansätze for the wavefunction, and how to exploit the method to minimize the energy of systems from 2 to 6 particles. 

Extensive benchmarks with other methods, including exact diagonalization and the Hartree-Fock approximation, will be discussed. In particular, I will discuss the emergence of two distinct physical phases depending on the sign of the interaction. Attractive systems show clear signs of bosonization, whereas in repulsive systems crystalline order appears.