Adaptive sampling design for multi-task learning of Gaussian processes in manufacturing

Approximation models (or surrogate models) have been widely used in engineering problems to mitigate the cost of running expensive experiments or simulations. Gaussian processes (GPs) are a popular tool used to construct these models due to their flexibility and computational tractability. The accuracy of these models is a strong function of the density and locations of the sampled points in the parametric space used for training. Previously, multi-task learning (MTL) has been used to learn similar-but-not-identical tasks together, thus increasing the effective density of training points. Also, several adaptive sampling strategies have been developed to identify regions of interest for intelligent sampling in single-task learning of GPs. While both these methods have addressed the density and location constraint separately, sampling design approaches for MTL are lacking. In this paper, we formulate an adaptive sampling strategy for MTL of GPs, thereby further improving data efficiency and modeling performance in GP. To this end, we develop variance measures for an MTL framework to effectively identify optimal sampling locations while learning multiple tasks simultaneously. We demonstrate the effectiveness of the proposed method using a case study on a real-world engine surface dataset. We observe that the proposed method leverages both MTL and intelligent sampling to significantly outperform state-of-the-art methods which use either approach separately. The developed sampling design strategy is readily applicable to many problems in various fields.