Physics-Informed Machine Learning Using Low-Fidelity Flowfields for Inverse Airfoil Shape Design

Physics-informed neural networks (PINNs) are a class of scientific machine learning that utilizes differential equations in loss formulations to model physical quantities. Despite recent developments, complex phenomena such as high-Reynolds-number (high-Re) flow remain a modeling challenge without the use of high-fidelity inputs. In this study, a low-fidelity-influenced physics-informed neural network (LF-PINN) is proposed as a surrogate aerodynamic analysis model for inverse airfoil shape design at Re=1.0x106. The LF-PINN is developed in a hybrid approach using low-fidelity flowfields approximated from a viscous-inviscid coupled airfoil analysis tool (mfoil) and physics residuals from the steady, incompressible, two-dimensional Navier-Stokes (NS) equations. The approach is designed to alleviate offline computational costs by avoiding high-fidelity simulations and sustain predicting accuracy using corrections by the physics residuals. The LF-PINN is able to correct the low-fidelity flowfield quantities toward the ground truth, with a mean improvement of about 19% in pressure and about 5% in total velocity based on Euclidean distance comparisons. Evaluation of the airfoil surface pressure coefficient Cp distributions shows corrections by the LF-PINN at the suction peak, which largely contributes to lifting forces. Inverse airfoil shape design is conducted using target Cp distributions in the objective function, whereby the LF-PINN can approach the expected target shapes while reducing online computational time by at least an order of magnitude compared to direct airfoil analysis tools.