Discrepancy Modeling with Intermediate Variables: A New Framework for Robust Gaussian Process Calibration

Abstract

Gaussian processes are widely used for surrogate modeling in computer experiments, which often produce numerous intermediate variables that are not explicitly used in standard calibration frameworks. Calibration of imperfect models can be challenging without leveraging these variables, while fitting the emulator and the discrepancy models separately also poses identifiability issues. In this work, we propose a robust Gaussian process calibration framework that leverages intermediate variables for discrepancy modeling. The framework integrates a structured intermediate variable selection process, a discretized scaled Gaussian stochastic process (S-GaSP) to constrain the discrepancy term, and a space-filling design strategy for selecting constraint points. This enables joint modeling of the emulator and discrepancy, improving predictive performance, providing principled uncertainty quantification, and alleviating identifiability risks. We demonstrate its efficacy on a nuclear physics application involving binding energies, where it outperforms baseline approaches.