In many scientific and engineering domains, physical experiments are often costly, time-consuming, and limited to a certain number of design points. The Kennedy and O'Hagan (KOH) framework is widely used for combining simulator runs with limited experimental observations. Under a Bayesian implementation, simulator output, model discrepancy, and observation noise are jointly modeled by coupled Gaussian processes, followed by posterior inference and uncertainty quantification, thereby providing a probabilistic foundation for experimental design. Existing sequential design criteria mainly target better parameter estimation or global uncertainty reduction but may overlook the local structure of the predicted response. This work presents a sequential Bayesian experimental design (BED) framework aimed at improving the predictive performance of the KOH model. The framework introduces a mutual information (MI)-based criterion combined with a local complexity score that measures nonlinearity of the posterior predictive mean near each candidate point, leading to more efficient design decisions. To make the criterion computationally feasible in a fully Bayesian setting, we employ Gaussian mixture reduction with fast covariance update strategies. Through several challenging test problems and an example of the Duffing oscillator on a discrete design space, we demonstrate the effectiveness of the proposed method and illustrate its difference from conventional design baselines under sequential (offline) and adaptive (online) BED settings. The numerical results suggest that incorporating local response complexity into the MI criterion can substantially improve prediction-oriented design for physical experiments informed by computer models.

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