Enhanced Hyperparameter Estimation for Gaussian Process Models in Experimental Design Applications

Adaptive experimental designs based on Bayesian Optimization effectively identify the conditions that best inform the experimental objective. A key component of these algorithms is Gaussian Process (GP) modeling, which relies on hyperparameter estimation, typically performed via log-likelihood maximization. However, due to the multimodal and unidentifiable nature of hyperparameters, this step is highly sensitive, and poor estimates can degrade GP performance, ultimately compromising experimental design efficiency. In this work, we demonstrate this sensitivity and propose three techniques to improve hyperparameter estimation. Our results show that these methods improve the accuracy of GP modeling, leading to more effective experimental designs. All analyses were performed on two test systems: a simulated reverse-water-gas shift reaction model and the synthetic Hartmann function.