应用数学和力学2026，Vol.47Issue(5)：655-667,13.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
Residual Splitting Adaptive Physics-Informed Neural Networks for Solving Partial Differential Equations
摘要
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 ad-dress 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 de-composition,and adopts a self-adaptive weighting strategy to automatically adjust the weights among the com-ponents,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 split-ting 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 superi-or computational efficiency.关键词
物理信息神经网络/自适应权重/残差分裂/区域分解Key words
physics-informed neural network/adaptive weighting/residual splitting/domain decomposition分类
数理科学引用本文复制引用
范昆昆,张皓然,岳煜铖,袁冬芳..残差分裂自适应物理信息神经网络求解偏微分方程[J].应用数学和力学,2026,47(5):655-667,13.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) （2022MS01008）
内蒙古科技大学基本研究业务费专项资金(2024QNJS052) （2024QNJS052）
