  Ice Ih, the common form of ice in the biosphere, contains proton disorder.
Its proton-ordered counterpart, ice XI, is thermodynamically stable below 72 K.
However, even below this temperature the formation of ice XI is kinetically
hindered and experimentally it is obtained by doping ice with KOH. Doping
creates ionic defects that promote the migration of protons and the associated
change in proton configuration. In this article, we mimic the effect of doping
in molecular dynamics simulations using a bias potential that enhances the
formation of ionic defects. The recombination of the ions thus formed proceeds
through fast migration of the hydroxide and results in the jump of protons
along a hydrogen bond loop. This provides a physical and expedite way to change
the proton configuration, and to accelerate diffusion in proton configuration
space. A key ingredient of this approach is a machine learning potential
trained with density functional theory data and capable of modeling molecular
dissociation. We exemplify the usefulness of this idea by studying the
order-disorder transition using an appropriate order parameter to distinguish
the proton environments in ice Ih and XI. We calculate the changes in free
energy, enthalpy, and entropy associated with the transition. Our estimated
entropy agrees with experiment within the error bars of our calculation.
