Gradient-Enhanced Multi-Output Gaussian Process Model for Simulation-Based Engineering Design

Abstract

The multi-output Gaussian process model has shown a promising way to deal with multiple related outputs. It can capture some useful information across outputs so as to provide more accurate predictions than simply modeling these outputs separately. If incorporating gradient formation into the modeling construction, the accuracy of the model can be further improved. The main original contribution of this work is to propose a multi-output Gaussian process model assisted by gradient information, which can enhance the prediction accuracies of multiple outputs simultaneously. The observed response values, as well as the gradient information of all the outputs, are incorporated in the covariance matrix. In such a structure, not only the observed responses but also the correlation information across different outputs can be fully used. The proposed model is demonstrated with two analytical examples and used for modeling aerodynamic coefficients of a NACA 0012 airfoil. Three other existing Gaussian-process-based models are also tested to compare with the proposed model. Results show that the proposed model is promising when it comes to the problems with multiple related outputs and the prediction accuracy can be enhanced with the help of gradient information.