摘要
在传统物理信息神经网络(physics-informed neural network,PINN)的基础上,通过融合维度扩展和多物理损失函数,提出了两种改进的偏微分方程求解方法,分别是:基于改进多层感知机的维度扩展物理信息神经网络(expanding physics-informed neural network with modified multi-layer perceptron,Em PINN)和多物理损失函数物理信息神经网络(diverse loss function physics-informed neural network,DL-PINN)。Em PINN创新性地提出了一种带有残差连接和维度扩展机制的神经网络结构,DL-PINN在Em PINN的基础上,将维度扩展机制、梯度增强物理信息与变分物理信息相结合,更有效地融入多种物理信息,进一步提高神经网络的拟合能力。实验结果表明,所提出的方法优于传统的物理信息神经网络方法,在不同偏微分方程案例上实现了最高两个数量级的求解精度提升。
Building upon the traditional PINN(physics-informed neural network),two improved methods for solving partial differential equations,EmPINN(expanding physics-informed neural network with modified multi-layer perceptron)and DL-PINN(diverse loss function physics-informed neural network),were presented by incorporating dimension expansion and diverse physics loss functions.EmPINN innovatively introduced a neural network structure with residual connections and a dimension-expanding mechanism.DL-PINN,based on EmPINN,combined the dimension-expanding mechanism with gradient enhancement and variational physical information to incorporate multiple physical information more effectively and improved the fitting capability of the neural network.Experimental results demonstrate that the proposed methods outperform traditional PINN method,improve solution accuracy by up to two orders of magnitude on different partial differential equation cases.
作者
任睿轩
黎铁军
金长松
陈新海
REN Ruixuan;LI Tiejun;JIN Changsong;CHEN Xinhai(College of Computer Science and Technology,National University of Defense Technology,Changsha 410073,China)
出处
《国防科技大学学报》
2025年第5期246-253,共8页
Journal of National University of Defense Technology
基金
国家自然科学基金资助项目(62072464)。
关键词
偏微分方程
物理信息神经网络
维度扩展
多物理损失函数
partial differential equations
physics-informed neural network
dimension-expanding
diverse physics loss functions
作者简介
第一作者:任睿轩(2000-),男,山东济南人,硕士研究生,E-mail:renruixuan18@nudt.edu.cn;通信作者:陈新海(1995-),男,四川眉山人,助理研究员,博士,E-mail:chenxinhai16@nudt.edu.cn。
