“…Phase transition process plays crucial roles in a variety of scientific, engineering, and industrial processes, including diamond crystal growth [1], the formation of mineral deposits, processing of advanced ceramic materials and coatings [2], weather forecasting [3], melt extraction from Earth's upper mantle [4,5,6], geochemical self-organization [7], and environmental contaminant transport [8]. The phase transition problems have been studied by different kinds of approaches: from experimental researches [4,9,10], to numerical simulations [11,12,13,14,3,15]; from solving partial differential equations [16,17,18,7,12,19], to statistical analysis [20,21,16,22], such as random network models to capture the stochastic nature of the phase transition process.…”