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In the realm of aircraft design, there is a prevalent need for surrogate modeling techniques capable of efficiently and accurately modeling objects with high evaluation costs and uneven sensitivity distributions, such as those encountered in the nonlinear buckling of thin-walled structures and aerodynamics at transonic speeds. However, the non-stationary Gaussian Process Regression (GPR) model requires extensive hyperparameters or judicious assumptions, limiting its applications in such tasks, and the commonly used K-Fold methodology suffers from inherent instability. Addressing these issues, this paper proposes an active learning method for surrogate modeling in systems featuring uneven sensitivity distribution, integrating non-stationary-noise GPR and K-Fold Artificial Neural Network (ANN) methodology, namely NSN-GPR-KF. Instead of relying on a non-stationary kernel function, the algorithm regards noise as a non-stationary factor within a stationary GPR framework, with noise levels estimated via the K-Fold ANN methodology, allowing GPR to efficiently adapt to non-stationary systems while avoiding the aforementioned requirements for non-stationary GPR. Case validations, performed on two test functions with pronounced uneven spatial sensitivity, demonstrate that NSN-GPR-KF outperforms commonly used stationary GPR and pure K-Fold methodology. It synthesizes the exploration capabilities of GPR with the exploitation proficiency of the K-Fold methodology, achieving comparable global accuracy with reduced sample sizes—up to 26 % and 22 % less than the other two algorithms, respectively. The algorithm was successfully applied to predict the buckling load of thin-walled pipe beams, demonstrating accelerated convergence and approximately 25 % greater accuracy compared to pure K-Fold model. These results suggest that NSN-GPR-KF can serve as an efficient and precise modeling tool for engineering tasks with high evaluation costs and complex sensitivity distributions. [ABSTRACT FROM AUTHOR]

As the "respiratory tract" of the air breathing engine, the hypersonic inlet plays the role of compressing, decelerating, and pressurizing flow. However, research on the traditional inlet design is mainly based on gas dynamics theory and experience, which not only leads to a long design period but also fails to ensure the performance of the inlet at non-design points under broad working conditions. In recent years, with the further development of flow physics, a variety of advanced inlet design methods have been proposed, and a large number of valuable data have been accumulated by applying high-fidelity computational fluid dynamics numerical simulation and ground wind tunnel tests. A new generation of machine learning technologies, typically represented by deep learning, is developing vigorously. By building a deep neural network structure and using data-driven methods to carry out model training, it can realize typical feature extraction automatically, efficiently, and accurately, which is helpful to deeply explore the hidden flow mechanism between data and establish a fast prediction model of inlet performance. The optimal inlet design scheme can be obtained by applying the performance intelligent prediction model and the multi-objective intelligent evolution algorithm. This paper provides a detailed overview of the latest progress in inlet design by applying traditional ideas, expounds the basic principles and typical applications of some representative and prospective machine learning methods, and especially reports the current research status of the combination of machine learning and inlet. Finally, the future development trends and potential applications of several research directions are summarized. [ABSTRACT FROM AUTHOR]