Adaptive Surrogate Models for Uncertainty Quantification with Partially Observed Information

Surrogate models are commonly used to reduce computational cost by replacing expensive physical models with much cheaper calculations. Gaussian process (GP) model exhibits superior performance among surrogate models due to the capability of estimating the uncertainty. However, the GP model often requires fully observed datasets for training. In many engineering applications, missing values often occur in the collected datasets, including data from different sources that have multi-fidelity or multi-dimensionality. Therefore, properly utilizing the partially observed information is essential in order to exploit all available information and increase the power of the model. To handle the missing value and partially observed information, this paper presents a new adaptive surrogate strategy employing the Bayesian Gaussian process latent variable model (BGPLVM) to make use of all available information, rather than using the fully observed part only. The efficiency of the surrogate model development process was further improved by a novel adaptive sampling approaches with partially observed information, which is proposed to select new training sample points and refine the model iteratively. To the best of the authors' knowledge, this is the first work designing adaptive surrogate modeling approaches for a dataset containing the missing value. The numerical experiments show that the proposed method can utilize all available information effectively including both fully and partially observed data. A much accurate prediction result is provided by the proposed adaptive surrogate strategy by taking advantage of extra partially observed information.