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To better understand the equilibrium $\gamma^\prime$(L1$_2$) precipitatemorphology in Co-based superalloys, a phase field modeling sensitivity analysisis conducted to examine how four phase-field parameters [initial Coconcentration ($c_0$), double-well barrier height ($\omega$), gradient energydensity coefficient ($\kappa$), and lattice misfit strain ($\epsilon_{\rmmisfit}$)] influence the $\gamma^\prime$(L1$_2$) precipitate size andmorphology. Gaussian Process Regression (GPR) models are used to fit the samplepoints and to generate surrogate models for both precipitate size andmorphology. In an Active Learning approach, a Bayesian Optimization algorithmis coupled with the GPR models to suggest new sample points to calculate andefficiently update the models based on a reduction of uncertainty. Thealgorithm has a user-defined objective, which controls the balance betweenexploration and exploitation for new suggested points. Our methodology providesa qualitative and quantitative relationship between the $\gamma^\prime$(L1$_2$)precipitate size and morphology and the four phase-field parameters, andconcludes that the most sensitive phase-field parameter for precipitate sizeand morphology is the initial Co concentration ($c_0$) and the double-wellbarrier height ($\omega$), respectively. We note that the GPR model forprecipitate morphology required adding a noise tolerance in order to avoidoverfitting due to irregularities in some of the simulated equilibrium$\gamma^\prime$(L1$_2$) precipitate morphology.

Active Learning Sensitivity Analysis of $\gamma^\prime$(L1$_2$) Precipitate Morphology of Ternary Co-Based Superalloys