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We compute the ground-state properties of fully polarized, trapped,one-dimensional fermionic systems interacting through a gaussian potential. Weuse an antisymmetric artificial neural network, or neural quantum state, as anansatz for the wavefunction and use machine learning techniques tovariationally minimize the energy of systems from 2 to 6 particles. We provideextensive benchmarks with other many-body methods, including exactdiagonalisation and the Hartree-Fock approximation. The neural quantum stateprovides the best energies across a wide range of interaction strengths. Wefind very different ground states depending on the sign of the interaction. Inthe non-perturbative repulsive regime, the system asymptotically reachescrystalline order. In contrast, the strongly attractive regime shows signs ofbosonization. The neural quantum state continuously learns these differentphases with an almost constant number of parameters and a very modest increasein computational time with the number of particles.

Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states