Inverse design model of airfoil based on long short-term memory neural network by fusing multi-position data

The airfoil inverse design is a crucial engineering challenge in the field of aerospace. The feature extraction capability of deep learning provides a new approach to address airfoil inverse design problems. This paper investigates the application of the long short-term memory (LSTM) neural network to airfoil inverse design under given local pressure coefficients (Cp) and friction coefficients (Cf). The database contains 625 samples for National Advisory Committee for Aeronautics airfoils at Mach numbers (Ma) from 0.2 to 0.5. Primarily, the mean relative error (MRE) for prediction is less than 0.94% when the sequence length parameter (λ) is set to 20%, suggesting the high precision of the LSTM model in airfoil inverse design. Then, the effects of the predicted location are analyzed in the present model. Subsequently, several sub-LSTM models are integrated, inspired by the Mixture of Experts approach. This multi-position long and short-term memory model (MP-LSTM) is aimed at addressing incomplete geometric predictions and fully utilizing the upstream and downstream information in the aerodynamic sequence, further reducing the MRE by 23%–0.724%. Finally, the MP-LSTM model is proven to reduce prediction errors up to 64% and 72% compared with previous convolutional neural network and conditional generative adversarial network models, respectively. This study presents an accurate local prediction model in airfoil inverse design rather than other global models, which is more flexible for further airfoil optimization.