基于低阶导数物理信息神经网络的流动和传热反演问题研究

Solving inverse problems of flow and heat transfer in aerodynamics is crucial for aircraft design and flight environment control. However, traditional numerical methods often encounter challenges related to computational complexity and data dependency when addressing such problems. To tackle these issues, based on the physics-informed neural network (PINN) framework, we present a low-order derivative physics-informed neural network (LPINN), which can effectively solve inverse problems in flow and heat transfer using only a limited amount of experimental measurement data. Two typical two-dimensional cases, namely Poiseuille flow and lid-driven cavity flow, are selected to comprehensively evaluate the effectiveness and reliability of LPINN in solving inverse problems. Results indicate that, without explicit boundary conditions, LPINN can accurately predict the flow and temperature fields within the entire computational domain using sparse observation data and can also precisely determine the unknown Reynolds and Péclet numbers in the governing equations. Comparisons of three observation point selection schemes —random, uniform, and prior-knowledge-based — reveal that the prior-knowledge-based scheme requires the fewest observation points to achieve high inversion accuracy, thereby enhancing the efficiency of solving inverse problems. Additionally, LPINN exhibits strong robustness against noise in experimental data.