Transfer Learning of Stochastic Kriging for Individualized Prediction.

Stochastic Kriging (SK) is a generalized variant of Gaussian process regression, and it is developed for dealing with non-i.i.d. noise in functional responses. Although SK has achieved substantial success in various engineering applications, its intrinsic modeling strategy by focusing on the sample mean limits its flexibility and capability of predicting individual functional samples. Moreover, the performance of SK can be impaired under scarce data scenarios, which are commonly encountered in engineering applications, especially for start-up or just deployed systems. In this paper, we propose a novel transfer learning framework to address the challenges of individualization and data scarcity in traditional SK. The proposed framework features a within-process model to facilitate individualized prediction and a between-process model to leverage information from related processes for resolving the issue of data scarcity. The within- and between-process models are integrated through a tailored convolution process, which quantifies interactions within and between processes using a specially designed covariance matrix and corresponding kernel parameters. Statistical properties are investigated on the parameter estimation of the proposed framework, which provide theoretical guarantees for the performance of transfer learning. The proposed method is compared with benchmark methods through various numerical and real case studies, and the results demonstrate the superiority of the proposed method in dealing with individualized prediction of functional responses, especially when limited data are available in the process of interest.