Abstract:
To solve the issue that conventional deep neural networks(DNN) needs prohibitively vast amount of data, the structure information contained in aerodynamic data needs to be fully utilized. Physics-informed neural network (PINN) is an unsupervised learning algorithm that uses deep neural networks to directly approximate solutions to partial differential equations (PDEs) of the flow fields, thus suitable for modeling aerodynamic problems. However, during the training process of PINN, the loss function only depicts the deviation of PDE at the training sample points, and for complex nonlinear partial differential equations, this deviation cannot accurately reflect the error between the function fitted by neural networks and the solution of PDEs. Moreover, errors inevitably exist in the boundary and initial conditions when fitted with neural networks, which accumulate in space and time, making the modeling accuracy of PINN less favorable compared to traditional models. In order to address the above issue, the present study integrates PINN with computational fluid dynamics (CFD) simulation results of the flow fields, which adds the deviation between PINN output and CFD value in the loss function at sampling points of the flow field, thus improving the modeling accuracy of the neural network. According to the model used in CFD simulations, the fusion mode can adopt instantaneous mode or time-averaged mode. Experimental results suggest that the proposed method can effectively improve the modeling accuracy of PINN.