On petascale systems, the selection of optimal values for I/O parameters without taking into account the I/O size and pattern can cause the I/O time to dominate the simulation time, compromising the application's scalability. In this paper, we adopt and adapt an engineering method called surrogate-based modeling to efficiently search for the optimal I/O parameter values and accurately predict the associated I/O times at the extreme scale. Our approach allows us to address both the search and prediction in a short time, even when the application's I/O is large and exhibits irregular patterns.