  Most water in the universe may be superionic, and its thermodynamic and
transport properties are crucial for planetary science but difficult to probe
experimentally or theoretically. We use machine learning and free energy
methods to overcome the limitations of quantum mechanical simulations, and
characterize hydrogen diffusion, superionic transitions, and phase behaviors of
water at extreme conditions. We predict that a close-packed superionic phase
with mixed stacking is stable over a wide temperature and pressure range, while
a body-centered cubic phase is only thermodynamically stable in a small window
but is kinetically favored. Our phase boundaries, which are consistent with the
existing-albeit scarce-experimental observations, help resolve the fractions of
insulating ice, different superionic phases, and liquid water inside of ice
giants.
