🤖 AI Summary
This work addresses the challenge of parameter optimization in computer model calibration, where the goal is to minimize discrepancies between multidimensional model outputs and observed data. The authors propose a novel root-finding paradigm that reformulates calibration as a root-search problem by constructing signed-residual-based Kriging or stochastic Kriging surrogates. Their approach integrates a sequential search space reduction strategy with a new acquisition function compatible with first-order optimizers. Notably, it guarantees algorithmic robustness even when roots may not exist—a scenario unaddressed by prior methods. Empirical evaluations demonstrate that the proposed method significantly outperforms conventional calibration techniques across both data-driven and physics-based modeling tasks, achieving higher computational efficiency while enhancing solution robustness.
📝 Abstract
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.