残差分裂自适应物理信息神经网络求解偏微分方程

范昆昆; 张皓然; 岳煜铖; 袁冬芳

doi:10.21656/1000-0887.460018

残差分裂自适应物理信息神经网络求解偏微分方程

doi: 10.21656/1000-0887.460018

1. 内蒙古科技大学自动化与电气工程学院，内蒙古包头 014010;
2. 内蒙古科技大学理学院，内蒙古包头 014010

基金项目:

国家自然科学基金地区科学基金(12261067

12361088)；内蒙古自然科学基金(2022MS01008)；内蒙古科技大学基本研究业务费专项资金(2024QNJS052)

详细信息

作者简介:
范昆昆（1998—），男，硕士生(E-mail: fankunkun914@163.com);袁冬芳（1985—），女，副教授，硕士（通信作者. E-mail: yuandf@imust.edu.cn）.

通讯作者:
袁冬芳（1985—），女，副教授，硕士（通信作者. E-mail: yuandf@imust.edu.cn）.

中图分类号: O241.82
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- 文章访问数: 16
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出版历程
- 收稿日期: 2025-01-24
- 修回日期: 2025-03-24
- 网络出版日期: 2026-06-04
- 刊出日期: 2026-05-01

Residual Splitting Adaptive Physics-Informed Neural Networks for Solving Partial Differential Equations

1. School of Automation and Electrical Engineering, Inner Mongolia University of Science and Technology, Baotou, Inner Mongolia 014010, P.R. China;
2. School of science, Inner Mongolia University of Science and Technology, Baotou, Inner Mongolia 014010, P.R. China

摘要

摘要: 物理信息神经网络(PINN)损失函数之间的量级差异，导致训练过程收敛缓慢，有时甚至会在某些区域训练失败.为解决这一挑战，本文提出了一种融合残差分裂和权重自适应的PINN模型.该方法通过将主导PINN训练过程的偏微分方程(PDE)残差项，按照区域分解的方式分裂为多个独立子项，并采用权重自适应加权策略，自动调节各个子项之间的权重，从而改善了PINN的收敛性.该方法弥补了全局残差策略忽略和抹平局部特征的缺陷，通过分裂子项的方式增加了对局部特征的关注，改善了优化过程的效率，从而提升了求解精度.数值实验结果表明，本文方法不仅在精度上超越了现有几种模型，且达到了2~3个数量级的提升，计算效率也表现出优越性能.
- 物理信息神经网络 /
- 自适应权重 /
- 残差分裂 /
- 区域分解
Abstract: The magnitude difference between the loss functions of physical-informed neural networks (PINN) leads to a slow convergence of the training process and sometimes even training failure in some regions. To address this challenge, a physical-informed neural network model incorporating residual splitting and weight self-adaptation was proposed. The method improves the convergence of PINN by splitting the residual terms of PDE dominating the training process of PINN, into multiple independent components according to the domain decomposition, and adopts a self-adaptive weighting strategy to automatically adjust the weights among the components, thus promoting the convergence of PINN. This method makes up for the defects of the global residual strategy ignoring and smoothing out the local features, and increases the attention to the local features by splitting the subterms, which improves the efficiency of the optimization process, and thus enhances the solution accuracy. Through numerical experiments, the results show that, the proposed method not only surpasses the existing models in terms of accuracy, but also achieves an improvement of 2-3 orders of magnitude with superior computational efficiency.
- physics-informed neural network /
- adaptive weighting /
- residual splitting /
- domain decomposition

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参考文献(30)

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残差分裂自适应物理信息神经网络求解偏微分方程

doi: 10.21656/1000-0887.460018

作者简介:
范昆昆（1998—），男，硕士生(E-mail: fankunkun914@163.com);袁冬芳（1985—），女，副教授，硕士（通信作者. E-mail: yuandf@imust.edu.cn）.

通讯作者:
袁冬芳（1985—），女，副教授，硕士（通信作者. E-mail: yuandf@imust.edu.cn）.

计量

Residual Splitting Adaptive Physics-Informed Neural Networks for Solving Partial Differential Equations

计量

目录

留言板

残差分裂自适应物理信息神经网络求解偏微分方程

doi: 10.21656/1000-0887.460018

作者简介: 范昆昆（1998—），男，硕士生(E-mail: fankunkun914@163.com);袁冬芳（1985—），女，副教授，硕士（通信作者. E-mail: yuandf@imust.edu.cn）.

通讯作者: 袁冬芳（1985—），女，副教授，硕士（通信作者. E-mail: yuandf@imust.edu.cn）.

计量

出版历程

Residual Splitting Adaptive Physics-Informed Neural Networks for Solving Partial Differential Equations

计量

出版历程

目录

作者简介:
范昆昆（1998—），男，硕士生(E-mail: fankunkun914@163.com);袁冬芳（1985—），女，副教授，硕士（通信作者. E-mail: yuandf@imust.edu.cn）.

通讯作者:
袁冬芳（1985—），女，副教授，硕士（通信作者. E-mail: yuandf@imust.edu.cn）.