Shrinkage-Constrained Functional Calibration for Complex Computer Models

2026-05-28

AI Summary

This work addresses the limitations of traditional KOH calibration methods, which suffer from insufficient regularization and parameter confounding under model mismatch, sparse data, and noise. The authors propose IBFU, a Bayesian calibration framework that models calibration parameters as the sum of fixed initial values and input-dependent Gaussian process correction terms. By incorporating strong shrinkage priors and orthogonality constraints, the approach enhances regularization while naturally extending the KOH framework to input-dependent calibration. This formulation preserves predictive accuracy and enables data-driven, spatially varying calibration mechanisms that activate adaptively based on empirical evidence. As a result, IBFU demonstrates markedly improved robustness, accuracy, and generalization in sparse and noisy scenarios.

Abstract

We propose a new Bayesian model calibration formalism as an alternative to the Kennedy O'Hagan (KOH) framework which we term integrated bias with full uncertainty (IBFU). In KOH, calibration parameters are modeled as fixed, but unknown distributions with relatively weak prior constraints, and their posteriors are inferred jointly with an additive discrepancy Gaussian Process (GP). This formulation often provides limited regularization and leads to confounding pathologies when applied to inexact models with sparse, noisy measurements. By contrast, we represent each calibration parameter as the sum of a fixed best estimate value and a parameter correction represented by an independent GP over the input space, equipped with strong shrinkage priors. Any residual discrepancy that cannot be addressed via parameter correction is captured by an additive discrepancy GP operating on the simulator, similar to KOH. We then impose orthogonality constraints to mitigate confounding between the simulator and modeled additive discrepancy and colinearity between model parameters. Imposing strong complexity shrinkage via conservative hyperpriors forces the mean parameter correction to remain flat across the domain, resulting in predictions that essentially converge with the KOH formulation. However, upon relaxing complexity shrinkage, should the data provide evidence that the effective calibration parameter varies across the domain, the mean parameter correction is allowed to become a function of the domain in a controlled, structured manner. In this sense, our approach is more universal: it effectively nests KOH as a special case while extending it to input dependent calibration, and it is more tightly constrained, because it anchors the true values around the best estimates and the shrinkage prior actively regularizes the calibration parameters.

Problem

• Bayesian calibration
• Kennedy-O'Hagan framework
• model discrepancy
• parameter confounding
• shrinkage priors

Innovation

• Bayesian calibration
• shrinkage prior
• Gaussian process
• input-dependent parameters
• model discrepancy