Transfer Learning of Stochastic Kriging for Individualized Prediction

Area of Science:

• Engineering
• Statistical Modeling
• Machine Learning

Background:

• Stochastic Kriging (SK) is a variant of Gaussian process regression for non-i.i.d. noise.
• Traditional SK struggles with individual prediction and data scarcity.
• Engineering applications often face limited data, especially for new systems.

Purpose of the Study:

• To propose a novel transfer learning framework for Stochastic Kriging.
• To address challenges in individualized prediction and data scarcity.
• To improve functional response prediction in data-limited scenarios.

Main Methods:

• Developed a transfer learning framework with within- and between-process models.
• Integrated models using a tailored convolution process with a custom covariance matrix.
• Investigated statistical properties for parameter estimation and theoretical guarantees.

Main Results:

• The proposed framework enables individualized prediction of functional responses.
• Effectively leverages information from related processes to overcome data scarcity.
• Demonstrated superiority over benchmark methods in numerical and real-world case studies.

Conclusions:

• The novel transfer learning framework significantly enhances Stochastic Kriging.
• It provides superior performance for individualized functional response prediction with limited data.
• Offers a robust solution for data-scarce engineering applications.