Fast flow field prediction of three-dimensional hypersonic vehicles using an improved Gaussian process regression algorithm

Conducting large-scale numerical computations to obtain flow field during the hypersonic vehicle engineering design phase can be excessively costly. Although deep learning algorithms enable rapid flow field prediction with high-precision, they require a significant investment in training samples, contradicting the motivation of reducing the cost of acquiring flow field. The combination of feature extraction algorithms and regression algorithms can also achieve high-precision prediction of flow fields, which is more suitable to tackle three-dimensional flow prediction with a small dataset. In this study, we propose a reduced-order model (ROM) for the three-dimensional hypersonic vehicle flow prediction utilizing proper orthogonal decomposition to extract representative features and Gaussian process regression with improved automatic kernel construction (AKC-GPR) to perform a nonlinear mapping of physical features for prediction. The selection of variables is based on sensitivity analysis and modal assurance criterion. The underlying relationship is unveiled between flow field variables and inflow conditions. The ROM exhibits high predictive accuracy, with mean absolute percentage error (MAPE) of total field less than 3.5%, when varying altitudes and Mach numbers. During angle of attack variations, the ROM only effectively reconstructs flow distribution by interpolation with a MAPE of 7.02%. The excellent small-sample fitting capability of our improved AKC-GPR algorithm is demonstrated by comparing with original AKC-GPRs with a maximum reduction in a MAPE of 35.28%. These promising findings suggest that the proposed ROM can serve as an effective approach for rapid and accurate vehicle flow predicting, enabling its application in engineering design analysis.