The detailed understanding of the high-pressure behavior of ammonia hydrates is a major challenge for planetary physics, as they are found in the composition of giant planets the solar system such as Neptune and Uranus. These mixtures present a variety of solid phases, some of which exhibit exotic properties such as plasticity or superionicity, as well as diverse forms of disorder (orientational, substitutional, translational and ionic disorder in particular). Though the phase diagram of ammonia hydrates is relatively well-known experimetally, theoretical studies remain scarce as the pose a huge simulation challenge that we propose to address by combining machine-learning (ML) interatomic potentials with accelerated sampling methods for free-energy calculations, as well as path-integral molecular dynamics (PIMD) to tackle nuclear quantum effects.