Sequential Bayesian Experimental Design for Prediction in Physical Experiments Informed by Computer Models

TL;DR

This paper introduces a sequential Bayesian experimental design framework for the Kennedy and O'Hagan model, utilizing mutual information and model complexity measures to enhance predictive accuracy efficiently in physical experiments.

Contribution

It develops a hybrid MI-based criterion combined with local complexity measures and proposes computational acceleration strategies, improving design efficiency and robustness over traditional methods.

Findings

The MI-based criterion outperforms IMSPE in early-stage uncertainty.

Hybrid design approach improves predictive performance.

Acceleration methods significantly reduce computational time.

Abstract

In many scientific and engineering domains, physical experiments are often costly, non-replicable, or time-consuming. The Kennedy and O'Hagan (KOH) model framework has become a widely used approach for combining simulator runs with limited experimental observations. Under a Bayesian implementation, the simulator output, model discrepancy, and observation noise are jointly modeled by coupled Gaussian processes, followed by coherent posterior inference and uncertainty quantification. This work presents a genuinely sequential Bayesian experimental design (BED) framework explicitly aimed at improving the predictive performance of the KOH model. We employ a mutual information (MI)-based criterion and develop a hybrid variant that integrates it with measures of local model complexity, leading to significantly more efficient design decisions. We further show theoretically that the MI-based criterion is more comprehensive and robust than the classical integrated mean squared prediction error (IMSPE) minimization criterion, especially when the model is highly uncertain in the early stages of the experiment. To mitigate the computational burden of fully Bayesian inference and the ensuing BED process, we propose two acceleration strategies - Gaussian Mixture Compression and Schur complement and rank-one update - which together substantially reduce runtime. Finally, we demonstrate the effectiveness of the proposed methods through both a synthetic example and a real biochemical case study, and compare them against several classical design criteria under sequential (offline) and adaptive (online) BED settings.