The data-driven deep active subspace method for aerodynamic prediction and analysis

The Active Subspace Method (ASM) struggles with gradient computation, making it challenging to determine reduced-dimensional subspace directions and limiting its effectiveness. To address this, this paper introduces the Deep Active Subspace Method (DASM) for aerodynamic prediction. By integrating Schmidt orthogonalization with deep neural networks, DASM formulates subspace directions as a specialized weight update mechanism and solves the reduced-dimensional subspace through backpropagation. DASM is validated against the Kriging model and ASM-Kriging reduced-order model. In transonic drag coefficient prediction for the RAE 2822 airfoil, DASM reduces design variables from 18 to 3 while achieving a 2.1% prediction error, outperforming ASM-Kriging (8.76%) and Kriging (3.94%). For the ONERA M6 and SACCON flying wing, DASM reduces 42 and 48 geometric variables to 1, respectively. Unlike ASM, DASM flexibly adjusts subspace dimensionality based on design needs. Increasing M6's subspace from 1 to 3 improves drag prediction to 1.56%, surpassing ASM-Kriging (3.97%) and Kriging (2.92%). A global sensitivity analysis shows DASM more accurately captures aerodynamic sensitivities, enhancing shape optimization by identifying key design variables. When combined with optimization algorithms, DASM accelerates convergence to the global optimum, demonstrating its potential for aerodynamic design.