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  

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

作　　者：张贤 胡春 崔永赫 王秋旺[2] 赵存陆 ZHANG Xian;HU Chun;CUI Yonghe;WANG Qiuwang;ZHAO Cunlu(State Nuclear Electric Power Planning Design&Research Institute CO.,Ltd.,Beijing 100095,China;MOE Key Laboratory of Thermo-Fluid Science and Engineering,School of Energy and Power Engineering,Xi'an Jiaotong University,Xi'an 710049,China)

机构地区：[1]国核电力规划设计研究院有限公司,北京100095 [2]西安交通大学热流科学与工程教育部重点实验室,西安710049

出　　处：《空气动力学学报》2025年第1期34-43,I0001,共11页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(51976157,51721004)。

摘　　要：求解空气动力学领域中流动和传热反演问题对于飞行器设计和飞行环境控制至关重要。然而,传统数值方法在处理这类问题时,往往面临计算复杂性和数据依赖性的挑战。为解决此问题,基于物理信息神经网络(PINN),本文构建了低阶导数物理信息神经网络(LPINN),其特点在于仅需有限的实验测量数据,即可有效地解决流动和传热的反演问题。为验证LPINN在反演问题上的应用效果,选择了两种典型的二维流动及传热案例(泊肃叶流动和顶盖驱动方腔流动)进行研究。结果表明,在缺乏明确边界条件的前提下,LPINN能利用稀疏的实验数据,准确预测整个计算区域内的流场和温度场,并能够较为精确地确定控制方程中的雷诺数和佩克莱数。对随机取点、均匀取点和基于先验知识取点3种不同的实验观测点选取方案进行了对比分析,发现基于先验知识取点方案在保证高反演精度的同时,其所需的实验观测点数量最少,这对提高反演问题的求解效率具有积极意义。此外,LPINN在处理反演问题时展现出对实验数据中噪声的高度鲁棒性。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.

关 键 词：低阶导数 物理信息神经网络 流动与传热 反演问题 

分 类 号：TK124[动力工程及工程热物理—工程热物理]