Bayesian Active Learning of Microstructure Transition in Rapid Solidification Using Phase-Field Simulations

This study investigates the mechanisms governing microstructure selection during rapid solidification, with a focus on the transition from cellular and dendritic to planar interface morphologies under conditions relevant to additive manufacturing. We employ a phase-field model that quantitatively captures solute trapping, kinetic undercooling, and morphological instabilities across a wide range of growth velocities (V) and thermal gradients (G), applying it to a binary Fe-Cr alloy as a surrogate for 316L stainless steel. By combining high-fidelity phase-field simulations with a Gaussian Process-based Bayesian active learning approach, we efficiently map microstructural transitions across the multidimensional space of composition, growth velocity, and temperature gradient. Our phase-field results are compared to classical theories of rapid solidification. In particular, the classical KGT model accurately predicts the critical value of G above which the interface remains planar at any growth velocity. We observe that microstructures evolve from dendritic to cellular as the temperature gradient approaches this critical G value. Additionally, we identify unstable "intermediate" microstructures near the dendrite-planar boundary at low G, even in the absence of banding instabilities in the Fe-Cr system. Such "intermediate" microstructures are difficult to identify with conventional design of experiments, however using Bayesian active learning methods, we have successfully identified this “transient” solidification regime. Overall, our results demonstrate the effectiveness of Bayesian-guided phase-field modeling in efficiently exploring complex microstructural transitions within high-dimensional parameter spaces, offering a powerful computational tool for tailoring process conditions to achieve desired microstructures and properties in rapidly solidified metallic alloys.