Goal-oriented Feature Extraction: a novel approach for enhancing data-driven surrogate model

Surrogate model can replace the parametric full-order model (FOM) by an approximation model, which can significantly improve the efficiency of optimization design and reduce the complexity of engineering systems. However, due to limitations in efficiency and accuracy, the applications of high-dimensional surrogate models are still challenging. In the present study, we propose a method for extracting hidden features to simplify high-dimensional problems, thereby improving the accuracy and robustness of surrogate models. We establish a goal-oriented feature extraction (GFE) neural network through indirect supervised learning. We constrained the distance between hidden features based on the differences in the target output. This means that in the hidden feature space, cases that are closer in distance output approximately the same, and vice versa. The proposed hidden feature learning method can significantly reduce the dimensionality and nonlinearity of the surrogate model, thereby improving modeling accuracy and generalization capability. To demonstrate the efficiency of our proposed ideas, We conducted numerical experiments on three popular surrogate models. The modeling results of typical high-dimensional mathematical cases and aerodynamic performance cases of ONERA M6 wings show that goal-oriented feature extraction significantly improves the modeling accuracy. Goal-oriented feature extraction can effectively reduce the error distribution of predicting cases and reduce the convergence and robustness differences caused by various data-driven surrogate models.