A persistent problem in the selective laser sintering process is to maintain the quality of additively manufactured parts, which can be attributed to the various sources of uncertainty. In this work, a two-particle phase-field microstructure model has been analyzed using a Gaussian process-based model. The sources of uncertainty as the two input parameters were surface diffusivity and interparticle distance. The response quantity of interest (QOI) was selected as the size of the neck region that develops between the two particles. Two different cases with equal and unequal-sized particles were studied. It was observed that the neck size increased with increasing surface diffusivity and decreased with increasing interparticle distance irrespective of particle size. Sensitivity analysis found that the interparticle distance has more influence on variation in neck size than that of surface diffusivity. The machine learning algorithm Gaussian process regression was used to create the surrogate model of the QOI. Bayesian optimization method was used to find optimal values of the input parameters. For equal-sized particles, optimization using Probability of Improvement provided optimal values of surface diffusivity and interparticle distance as 23.8268 and 40.0001, respectively. The Expected Improvement as an acquisition function gave optimal values of 23.9874 and 40.7428, respectively. For unequal-sized particles, optimal design values from Probability of Improvement were 23.9700 and 33.3005, respectively, while those from Expected Improvement were 23.9893 and 33.9627, respectively. The optimization results from the two different acquisition functions seemed to be in good agreement.