Hyperparameter Optimisation of Physics-Informed Neural Network using Particle Swarm Optimisation for predicting Lift and Drag Coefficient of NACA Airfoils.

In the present research, the Physics-Informed Neural Network (PINNs) is applied alongside Particle Swarm Optimisation (PSO) to predict the aerodynamic coefficients of NACA airfoils. The base PINN is a solver that solves the steady state, incompressible, two-dimensional Navier-Stokes equation in a meshless form that consists of the continuity equation, the x and y momentum equations, and appropriate boundary conditions as a constraint on the loss function. The PSO module is an automated selection of 9 significant hyperparameters, such as learning rate, 6 physicsloss weights, and 2 scaling factors for collocation density, based on a low-cost proxy network. Ten NACA airfoils from three geometric families (four-digit, five-digit and six-series) are tested at angles of attack 0° to 10°, and a Reynolds number of 100,000. The stages are optimised using a three-stage Reynolds number program (Re = 20,000 → 50,000 → 100,000) and a two-stage optimisation scheme (Adam followed by Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS)). The PINN model achieved an RMSE of 0.0342 and an R2 of 0.9925 for aerodynamiccoefficient prediction across multiple NACA airfoil profiles, with drag and lift predictions yielding R2 values of 0.9594 and 0.9891, respectively. Upon integrating PSO for hyperparameter tuning, the PINNs + PSO hybrid reduced the overall RMSE by approximately 48.7% for CL and 47.2% for CD relative to the baseline PINNs, achieving a final RMSE of 0.01754 for combined aerodynamic coefficients, while the R2 improved to 0.9980. The drag R2 increased from 0.9594 to 0.9887 (~2.93% gain) and the lift R2 from 0.9891 to 0.9971 (~0.80% gain). These results imply that PSO can yield substantial accuracy gains in PINNs that are systematically trained for aerodynamic prediction, even when the underlying network architecture is not altered.