Physics-Informed Machine Learning for Inverse Airfoil Shape Design

Abstract

In this study, a physics-informed machine learning aerodynamic flow prediction model is developed for inverse airfoil shape design. The machine learning model is trained using a hybrid implementation of low-order flow field information and physical governing equation residuals. A low-fidelity coupled panel method – boundary layer model embedded in MFOIL is used to compute low-order flow fields of a large database of airfoil shapes to construct the scarce input data for training a Physics-Informed Neural Network (PINN) driven by incompressible, two-dimensional Navier-Stokes (NS) equations. The PINN-predicted pressure field and airfoil surface pressure coefficient distribution (Cp) show improvements over fully data-driven alternatives and the low-order solution when compared against high-order CFD solutions computed from OpenFOAM. An inverse airfoil shape design is illustrated using this machine learning surrogate based on the target Cp distribution as the objective function, whereby the PINN can converge towards the target airfoil shape with fewer function evaluations than data-driven alternatives and direct airfoil analysis.