There are several fresh, promising approaches for solving partial differential equations (PDEs) based on machine learning techniques. In this study, the physics-informed neural network (PINN) is applied to approximate the solution of the full potential equation to simulate airfoil computation. To deal with a PDE system, PINN is capable of working without partial differentiation of the equation and specifically deals with shocks, which mainly uses the physical equations and other constraints like boundary conditions. The PINN method is efficient in solving PDEs, especially in higher dimensions, while it seems impossible to tackle them using traditional numerical methods due to the complex mesh generations and formulations. For the PINN method, the solution of this PDE system is predicted by DNN. The network architecture contains four hidden layers, using the tanh() function as the activation function. It is capable to take a spatial–temporal point as input so that the mean-square error is obtained to calculate loss terms. Then an optimizer is used to specify the mapping between the input and output. To show how well PINN performs in solving the full potential equation for various free-stream Mach number values, three examples are used. The predicted results show that PINN can find solutions successfully. Furthermore, several methods are proposed to optimize our model.
Solution of the Full Potential Equation on an Airfoil by Physics-Informed Neural Network
Lect.Notes Mechanical Engineering
International conference on Advancement in Materials, Manufacturing, and Energy Engineering ; 2022 ; Xi'an, China September 23, 2022 - September 25, 2022
Recent Advances in Applied Mechanics and Mechanical Engineering ; Chapter : 22 ; 215-225
2023-08-09
11 pages
Article/Chapter (Book)
Electronic Resource
English