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.

翻译：在许多科学与工程领域中，物理实验往往成本高昂、不可复现或耗时漫长。Kennedy和O'Hagan（KOH）模型框架已成为一种广泛使用的方法，用于将模拟器运行结果与有限的实验观测数据相结合。在贝叶斯实现框架下，模拟器输出、模型偏差和观测噪声通过耦合高斯过程进行联合建模，进而实现连贯的后验推断与不确定性量化。本文提出了一种真正意义上的序贯贝叶斯实验设计（BED）框架，其明确目标在于提升KOH模型的预测性能。我们采用基于互信息（MI）的准则，并开发了一种将其与局部模型复杂度度量相结合的混合变体，从而显著提升设计决策的效率。进一步，我们从理论上证明，与经典的积分均方预测误差（IMSPE）最小化准则相比，基于MI的准则更加全面且鲁棒，尤其在实验早期阶段模型高度不确定的情况下。为缓解完全贝叶斯推断及后续BED过程的计算负担，我们提出了两种加速策略——高斯混合压缩以及Schur补与秩一更新——二者共同大幅缩短了运行时间。最后，我们通过一个合成示例和一个真实生物化学案例研究，展示了所提方法的有效性，并在序贯（离线）与自适应（在线）BED设定下将其与若干经典设计准则进行了对比。