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