Euler equation embedded machine learning method for wall pressure and skin friction distribution

Rapid and accurate assessment of aerodynamic performance is essential for aircraft design. Key factors affecting aerodynamic performance include pressure and skin friction forces, which are critical distributed loads in aerodynamic shape optimization and structural analysis. Traditional methods for determining these loads rely heavily on numerical simulations, which are time-consuming and highly sensitive to mesh quality and turbulence modelling choices. Conventional machine learning methods, on the other hand, often require a large amount of training data and may suffer from poor generalization. To address these limitations, this paper presents a machine learning framework that integrates solutions from the Euler equations to predict wall aerodynamic forces. By embedding inviscid flow characteristics into the machine learning model, this approach leverages the inherent physical knowledge of Euler solutions to enhance both accuracy and generalizability, even with a modest dataset. The effectiveness of this method is demonstrated through tests on standard 2D aerofoil and 3D wing geometries under subsonic and transonic flow conditions, showing strong extrapolation capabilities for cases with varying flow states and geometries. This hybrid modelling approach not only achieves high accuracy with a significantly reduced dataset but also effectively reduces prediction error, keeping drag error within approximately 3%.