Unsteady reduced order model with neural networks and flight-physics-based regularization for aerodynamic applications

Numerical simulation of unsteady fluid flow plays an important role in several areas of the aeronautical industry. Since high-fidelity computational fluid dynamics simulations could be prohibitive in terms of computational cost, data-driven reduced order models become a suitable alternative for efficiently predicting flow variables as long as the accuracy of such models is comparable to that obtained by the full order model counterpart. This is especially important for iterative design purposes, where a few target variables must be evaluated on a large number of possible parameters. Therefore, we propose a neural network based methodology to develop an unsteady reduced order model of the subsonic/transonic flow field on 2D aerodynamic profiles trained on high-fidelity computational fluid dynamics data. For the purpose of dimensionality reduction, either proper-orthogonal decomposition or autoencoders are employed. For the regression task, a gated recurrent unit neural network is used to map an unsteady Schroeder multi-sine signal of angle of attack along with its first and second time-derivatives to the solution of surface variables, such as coefficients of pressure and friction. In order to shed light on the inner workings of data-driven methods so it could be employed in the aircraft design process, we introduce a flight-physics-based regularization term to incorporate information about the calculation of integral coefficients, like drag and lift, into the machine learning training workflow. Using our method, airfoil flow variables of interest can be predicted at a fraction of the cost of classical methods without any considerable accuracy loss. We also provide a comparison between reduction methods and we show evidence that supports the use of the proposed flight-physics-based regularization for building unsteady reduced order models based on machine learning.