  Water absorption and dissociation processes on pristine low-index TiO$_2$
interfaces are important but poorly understood outside the well-studied anatase
(101) and rutile (110). To understand these, we construct three sets of machine
learning potentials that are simultaneously applicable to various TiO$_2$
surfaces, based on three density-functional-theory approximations. We compute
the water dissociation free energies on seven pristine TiO$_2$ surfaces, and
predict that anatase (100), anatase (110), rutile (001), and rutile (011)
surfaces favor water dissociation, anatase (101) and rutile (100) surfaces have
mostly molecular absorption, while the calculated dissociation fraction on
rutile (110) surface may depend on the density functional assumed. Moreover,
using an automated algorithm, we reveal that these surfaces follow different
types of atomistic mechanisms for proton transfer and water dissociation:
one-step, two-step, or both. Our finding thus demonstrates that the different
pristine TiO$_2$ surfaces react with water in distinct ways, and cannot be
represented using just the low-energy anatase (101) and rutile (110) surfaces.
