A deep neural network reduced order model for unsteady aerodynamics of pitching airfoils

A machine learning framework is developed to compute the aerodynamic forces and moment coefficients for a pitching NACA0012 airfoil incurring in light and deep dynamic stall. Four deep neural network frameworks of increasing complexity are investigated: two multilayer perceptrons and two convolutional neural networks. The convolutional framework, in addition to the standard mean squared error loss, features an improved loss function to compute the airfoil loads. In total, five models are investigated of increasingly complexity. The convolutional model, coupled with the loss function based on force and moment coefficients and embedding the attention mechanism, is found to robustly and efficiently predict pressure and skin friction distributions over the airfoil over the entire pitching cycle. Periodic conditions are implemented to grant the physical smoothness of the model output both in space and time. An analysis of the training dataset point distributions is performed to point out the effects of adopting low discrepancy sequences, such as Latin hypercube, Sobol', and Halton, compared to random and uniform sequences. The current model shows improved performances in predicting forces and pitching moment in a broad range of operating conditions.