A new Gaussian process regression model using an approximate best linear unbiased predictor for handling large data

Abstract

A surrogate model is the alternative to an actual test or simulation model that incurs higher costs and needs more time to perform a single analysis. It is a mathematical model using which the test model’s outcome can be obtained at a more affordable cost. To produce a surrogate model, there must be information regarding several training points in the domain. Earlier, training points were placed in the domain using a design of experiments to obtain information and calculate the true responses from these training points. However, numerous studies are now utilizing the experimental and computational simulation data that has accumulated in the industry over time. Hence, the surrogate model field is actively conducting research on data-driven surrogate models that generate surrogate models using the large quantity of pre-accumulated data, rather than data that was obtained using experimental design. However, the size of data used in the existing data-driven surrogate models limits the types of models that can be used. One of these models includes the best linear unbiased predictor (BLUP), which is a Gaussian process-based surrogate model. As a surrogate model, BLUP has an outstanding prediction performance, it, however, starts encountering difficulties in generating models as the data size increases because it involves the process of calculating the inverse of matrices. Therefore, the data-driven surrogate model field uses a machine learning (ML)-based surrogate model that does not require this inverse calculation; however, the ML-based surrogate model is unable to offer the same prediction performance as BLUP, which limits its applicability in the field of engineering design. To resolve these issues, this study proposes an approximate BLUP (ABLUP), which is a new version of BLUP with outstanding prediction performance that can handle large data. The proposed method presents the concept of composite likelihood function that is used when large data is handled in the statistical inference field. A new BLUP was deduced and an equation was obtained based on this concept. This study also establishes a detailed model generation process to ensure that the equation can be applied to actual problems. The final goal of the proposed ABLUP is to generate a model from a data domain of a size that the Gaussian process-based surrogate models cannot handle with a better prediction performance than the machine learning-based methods equipped to handle large data. ABLUP’s performance was verified by applying the model to six different benchmark test problems with various trends. Moreover, the results and prediction performances of other methods were compared to prove ABLUP’s superiority.