Study of inverse problems of flow and heat transfer using low-order derivative physics-informed neural network

Solving inversion problems of flow and heat transfer in the field of aerodynamics is crucial for aircraft design and flight environment control. However, traditional numerical methods often face challenges in computational complexity and data dependency when dealing with such problems. To address this issue, based on the physical information neural network (PINN), the present study builds a low-order derivative physical information neural network (LPINN) that can solve flow and heat transfer inverse problems using only a small amount of measurement data. Two typical two-dimensional flows and heat transfer problems, i.e., Poiseuille flow and lid-driven cavity flow, are used to comprehensively test the effectiveness and reliability of LPINN in solving inverse problems. The results show that in the case of unknown boundary conditions, LPINN can accurately predict the flow and temperature fields within the entire computational domain using only sparse observation data, and can also accurately determine the unknown Reynolds and Peclet numbers in the governing equations. By comparing and analyzing the reverse results under three schemes of observation point selection, i.e., random point selection, uniform point selection, and prior knowledge point selection, it is found that the scheme of prior knowledge point selection requires the smallest number of observation points to preserve a certain high inversion accuracy; which is helpful to enhance the efficiency in solving inverse problems. Furthermore, LPINN demonstrates strong robustness in inverse problems as it is insensitive to experimental data noise.