Complex $\mathrm{Ga}_{2}\mathrm{O}_{3}$ Polymorphs Explored by Accurate and General-Purpose Machine-Learning Interatomic Potentials

$\mathrm{Ga}_{2}\mathrm{O}_{3}$ 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.