Goal-Oriented Feature Extraction: A Novel Approach to Enhance Data-Driven Surrogate Models

Surrogate models can replace the parametric full-order model (FOM) with an approximation model, which can significantly improve the efficiency of optimization and reduce the complexity of engineering systems. However, due to limitations in efficiency and accuracy, the applications of high-dimensional surrogate models remain challenging. In the present study, we propose a method to extract hidden features to simplify high-dimensional problems and improve the accuracy and robustness of surrogate models. We establish a goal-oriented feature extraction neural network using indirect supervised learning. Then, we constrain the distance between hidden features based on differences in the target output. The proposed hidden-feature learning method can significantly reduce the dimensionality and nonlinearity of the surrogate model to improve the modeling accuracy and generalization capability. To demonstrate the efficiency of our proposed ideas, we conduct numerical experiments on three popular surrogate models. The modeling results of typical high-dimensional mathematical cases and aerodynamic performance cases of RAE2822 airfoils and ONERA M6 wings show that goal-oriented feature extraction significantly improves the modeling accuracy. Goal-oriented feature extraction can also effectively reduce the error distribution of prediction cases and the differences in convergence and robustness caused by different data-driven surrogate models.