Bayesian-Entropy Gaussian Process For Constrained Metamodeling

A novel Bayesian-Entropy Gaussian Process (BEGP) is proposed for constrained metamodeling. Gaussian Process (GP) regression is a flexible and robust tool for surrogate modeling using observation data. For many engineering problems, available information other than observations may be known, such as physical constraints, boundary conditions, and empirical knowledge. Based on the Bayesian-Entropy (BE) principle, this paper introduces a novel framework for encoding extra information in addition to point data in constructing a GP regression model. The extra information is treated as constraints on the mean prediction of GP. The BE method can rigorously incorporate extra information as constraints into classical Bayesian framework. The constraint term is added into the posterior distribution of the hyperparameters when training the GP model. BEGP serves as an information fusion tool to enhance the extrapolation behavior of the GP model by incorporating additional knowledge about the problem. The proposed methodology is demonstrated on a numerical toy example and a structural analysis example highlighting the ability to smoothly connect two local GPs and incorporate boundary conditions as extra constraints. The BEGP shows the ability of incorporating physics constraints to enhance prediction and extrapolation behaviors. Finally, conclusions and future work are drawn based on the proposed study.