PINNs Method for Parameter Inversion Problem of Three-Dimensional Steady-State Heat Conduction Equation

热传导反问题广泛应用于地球科学、医学等领域，本文基于内嵌物理机理神经网络(PINNs)研究了一类三维有界域上热传导方程参数反演问题的数值解法。构建三维参数辨识模型，提出基于PINNs求解立方体区域三维稳态热传导方程参数反演问题的算法。通过同步反演热传导系数与整体温度值，实现热物性参数的高精度识别。在含噪声数据条件下，热传导系数反演的误差精度控制在10−4数量级，证实了算法对病态问题具有良好的抗噪性。Inverse heat conduction problem is widely used in earth science, medicine and other fields. In this paper, based on embedded physical mechanism neural network (PINNs), a numerical method for parameter inversion of heat conduction equation in three-dimensional bounded domain is studied. A three-dimensional parameter identification model is established, and an algorithm based on PINNs is proposed to solve the parameter inversion problem of three-dimensional steady-state heat conduction equation in cube region. Through simultaneous inversion of heat transfer coefficient and global temperature value, high precision identification of thermal physical property parameters is realized. Under the condition of noisy data, the error accuracy of heat transfer coefficient inversion is controlled at the order of 10−4, which proves that the algorithm has good anti-noise performance for ill-conditioned problems.