广东工业大学学报2025，Vol.42Issue(6)：70-77,125,9.DOI:10.12052/gdutxb.240155
各向异性扩散方程的神经网络算法
Neural Network Algorithms for Awonisotropic Diffusion Equations
摘要
Abstract
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.关键词
各向异性/扩散方程/物理信息神经网络/预测精度Key words
anisotropic/diffusion equation/physics-informed neural network/predictive accuracy分类
计算机与自动化引用本文复制引用
欧阳浩聪,房金伟..各向异性扩散方程的神经网络算法[J].广东工业大学学报,2025,42(6):70-77,125,9.基金项目
国家自然科学基金青年基金资助项目(12001115) （12001115）
广州市科技计划项目(202201010648) （202201010648）
