We concern computer model calibration problem where the goal is to find the parameters that minimize the discrepancy between the multivariate real-world and computer model outputs. We propose to solve an approximation using signed residuals that enables a root finding approach and an accelerated search. We characterize the distance of the solutions to the approximation from the solutions of the original problem for the strongly-convex objective functions, showing that it depends on variability of the signed residuals across output dimensions, as wells as their variance and covariance. We develop a metamodel-based root finding framework under kriging and stochastic kriging that is augmented with a sequential search space reduction. We derive three new acquisition functions for finding roots of the approximate problem along with their derivatives usable by first-order solvers. Compared to kriging, stochastic kriging accounts for observational noise, promoting more robust solutions. We also analyze the case where a root may not exist. Our analysis of the asymptotic behavior in this context show that, since existence of roots in the approximation problem may not be known a priori, using new acquisition functions will not compromise the outcome. Numerical experiments on data-driven and physics-based examples demonstrate significant computational gains over standard calibration approaches.

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