A Neural Network Method For A Class Of Heat Source Inverse Problems

A numerical method based on neural network is proposed to solve the shape inverse source problem for a class of parabolic equations.Its practical significance is that the location and shape of the heat source can be determined by measuring the temperature and heat flux of the outer boundary.We first introduce a general objective functional for solving this class of problems.Then we obtain a reasonable loss function of neural networks from the objective functional by finite element method.Moreover,we con-sider different network structures,initialization method,training step and other neural network related construction and training methods to solve successfully the problem.Finally,two and three-dimensional examples are given to illustrate the effectiveness of this method.