求解有源汇单相渗流方程的高效物理信息残差神经网络  

An Efficient Physics-informed Residual Neural Network for Solving Seepage Squation with Source Term

作　　者：汪欢 李道伦[1] WANG Huan;LI Daolun(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院,合肥230601

出　　处：《大学数学》2024年第5期8-15,共8页College Mathematics

基　　金：国家自然科学基金(12172115);国家自然科学基金(12372244)。

摘　　要：文章基于深度学习方法,提出一种高效的物理信息残差网络,用于求解渗流方程.该网络构造了独特的残差结构,并结合自回归、梯度衰减、变时间步长等策略训练模型.数值实验表明,本文方法能有效解决均质与非均质问题.与基线方法相比,本方法的求解时间减少50%.此外,本方法对不同渗透率、流量的算例无需调整网络参数,展现出了良好的鲁棒性和泛化能力.This paper proposes an efficient physics-informed residual neural network(E-PIResNet)based on deep learning metho d s.The network constructs a unique residual structure and combines strategies such as autoregression,gradient decay,and variable time steps for model training.Numerical experiments show that this method effectively solves both homogeneous and heterogeneous problems.Compared to baseline metho d s,this approach reduces solution time by 50%.Additionally,this method demonstrates good robustness and generalization capabilities across examples with different permeabilities and flow rates without needing to adjust network parameters.

关 键 词：渗流方程 物理信息 残差神经网络 自回归 跳跃连接 

分 类 号：O241.82[理学—计算数学]