Adaptive surrogate models with partially observed information

Surrogate models have been developed to replace expensive physical models and reduce the computational cost in various engineering applications, such as reliability analysis and uncertainty quantification. Gaussian process (GP) model exhibits superior performance among surrogate models with a distinguishing feature of estimating the uncertainty. However, fully observed datasets are generally required to establish a GP model, which is often scarce and expensive to obtain in complex engineering systems. Partially overserved information is often available and relatively plentiful in the collected datasets, which often contain data from different sources that have multi-fidelity or dimensionality and missing values. Therefore, correctly accounting for the partially observed information is important in order to take advantage of all available information and increase the prediction performance of the surrogate model to be developed. This paper presents a new method for modeling system performance with partially observed information, which integrates the Bayesian Gaussian process latent variable model (BGPLVM) with adaptive sampling to iteratively select new partially observable training sample points to improve the modeling efficiency. A novel adaptive sampling approach considering the missing frame and information cost of the partially observed information is proposed to iteratively select new training sample points and refine the model. To the best of the authors' knowledge, this is the first work designing adaptive sampling and adaptive surrogate modeling approaches for a dataset containing missing values. The numerical experiments demonstrated that the adaptive surrogate modeling method can effectively use all available information including both fully observed and partially observed data points. The developed methodology provides an accurate and cost-effective solution to take advantage of extra partially observed information in developing surrogate models.