各向异性扩散方程的神经网络算法

欧阳浩聪; 房金伟

doi:10.12052/gdutxb.240155

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各向异性扩散方程的神经网络算法

计算机科学与技术 | 更新时间：2026-05-27

- 各向异性扩散方程的神经网络算法
- Neural Network Algorithms for Awonisotropic Diffusion Equations
- 广东工业大学学报 2025年42卷第6期页码：70-77, 125
- 作者机构：
  
  广东工业大学数学与统计学院,广东,广州,510520
- 作者简介：
  
  欧阳浩聪(2000–) ，男，硕士研究生，主要研究方向为偏微分方程数值解，E-mail：928959811@qq.com
  房金伟(1987–) ，男，讲师，博士，主要研究方向为偏微分方程数值解，E-mail：fangjinwei@gdut.edu.cn
- 基金信息：
  
  国家自然科学基金青年基金资助项目(12001115);广州市科技计划项目(202201010648)
- DOI：10.12052/gdutxb.240155
  中图分类号： TP183
- 纸质出版：2025
- 稿件说明：
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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.

Ouyang Haocong, Fang Jinwei. Neural Network Algorithms for Awonisotropic Diffusion Equations[J]. 2025, 42(6): 70-77, 125.
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. DOI： 10.12052/gdutxb.240155

Ouyang Haocong, Fang Jinwei. Neural Network Algorithms for Awonisotropic Diffusion Equations[J]. 2025, 42(6): 70-77, 125. DOI： 10.12052/gdutxb.240155.

摘要

基于物理信息神经网络(Physics-Informed Neural Network

PINN) 求解各向异性扩散方程。首先提出了垂直平行采样法，对材料坐标系的不同方向进行数据点采集。实验结果表明，相比传统的随机采样方法，该方法能够准确捕捉问题中各向异性变化特性，提高神经网络预测精度。其次提出了加权积分离散法，与普通的PINN方法不同，该方法将计算数据点误差改为计算积分型误差函数，通过嵌入权函数并使用高斯积分数值方法进行离散。实验结果表明，使用该方法预测的结果准确性具有较大的提升，并且收敛稳定性更强和收敛速度更快。

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

Keywords

references

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