  $\mathrm{Ga}_{2}\mathrm{O}_{3}$ is a wide-bandgap semiconductor of emergent
importance for applications in electronics and optoelectronics. However, vital
information of the properties of complex coexisting
$\mathrm{Ga}_{2}\mathrm{O}_{3}$ polymorphs and low-symmetry disordered
structures is missing. In this work, we develop two types of kernel-based
machine-learning Gaussian approximation potentials (ML-GAPs) for
$\mathrm{Ga}_{2}\mathrm{O}_{3}$ with high accuracy for
$\beta$/$\kappa$/$\alpha$/$\delta$/$\gamma$ polymorphs and generality for
disordered stoichiometric structures. We release two versions of interatomic
potentials in parallel, namely soapGAP and tabGAP, for excellent accuracy and
exceeding speedup, respectively. We systematically show that both the soapGAP
and tabGAP can reproduce the structural properties of all the five polymorphs
in an exceptional agreement with ab initio results, meanwhile boost the
computational efficiency with $5\times10^{2}$ and $2\times10^{5}$ computing
speed increases compared to density functional theory, respectively. The
results show that the liquid-solid phase transition proceeds in three different
stages, a "slow transition", "fast transition" and "only Ga migration". We show
that this complex dynamics can be understood in terms of different behavior of
O and Ga sublattices in the interfacial layer.
