Neural Network Algorithms for Awonisotropic Diffusion Equations

In this research, the anisotropic diffusion equation is solved based on physics-informed neural network (PINN) . Firstly, a vertical parallel sampling method is proposed to collect data points in different directions of the material coordinate system. The experimental results show that the method can accurately capture the anisotropic variation characteristics in the problem and improve the prediction accuracy of the neural network compared with the traditional random sampling method. Secondly, the weighted integral discretization method is proposed, which is different from the ordinary PINN method in that it changes the calculation of the data point error to the calculation of the integral-type error function, which is discretized by embedding the weight function and using the Gaussian integral numerical method. The experimental results show that the accuracy of the predicted results using this method has a significant improvement, and the convergence stability is stronger and the convergence speed is faster.