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

2026-06-10

AI Summary

This study addresses the limitations of traditional Gaussian process (GP) calibration methods, which neglect intermediate variables in computer experiments, leading to inadequate bias modeling and non-identifiability between the simulator and the discrepancy term. To resolve this, the authors propose a robust GP calibration framework that explicitly incorporates intermediate variables. The approach systematically selects key intermediate variables, constrains the discrepancy term using a scaled Gaussian stochastic process (S-GaSP), and employs space-filling designs to choose constraint points, thereby enabling identifiable joint modeling of the simulator and bias. This work is the first to systematically integrate intermediate variables into GP calibration, substantially improving predictive accuracy and the reliability of uncertainty quantification. Empirical results on nuclear binding energy prediction demonstrate clear superiority over existing baseline methods.

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.

Problem

• Gaussian process calibration
• intermediate variables
• discrepancy modeling
• identifiability
• computer experiments

Innovation

• intermediate variables
• Gaussian process calibration
• discrepancy modeling
• S-GaSP
• identifiability