Thanks Sanjayk! Regarding your questions:

1. I've chosen the standard Gaussian kernel in the current case study as it is the most popular one in engineering domain. In general machine learning, Matern kernel is more frequently used. To learn more about the characteristics of various kernels, I would recommend the book "Gaussian Processes for Machine Learning", C. E. Rasmussen & C. K. I. Williams, Chapter 4.

2. The first thing that came to my mind is when the number of design parameters is large. When that happens, more iterations are required to reach the global optimum. Also, each iteration will cost more, as fitting a high-dimensional surrogate model is not cheap.