山东理工大学学报（自然科学版）2025，Vol.39Issue(4)：47-53,7.
局部自适应物理信息神经网络在求解Burgers-Fisher方程中的应用
Application of locally adaptive physics-informed neural networks in solving the Burgers-Fisher equation
摘要
Abstract
Aiming at the limitations of physics-informed neural networks(PINNs)in terms of training efficiency and solving accuracy,an improved PINNs model is proposed.This model introduces adjustable parameters into each neuron which allows the neural network to flexibly approximate nonlinear discontinu-ous functions.Consequently,the solution error of the neural network is reduced by 2～3 orders of magni-tude,and the PINNs'solution error is reduced by approximately one order of magnitude,significantly im-proving the accuracy in solving the Burgers-Fisher equation.This study also explores the effects of differ-ent scaling factors on model performance.When appropriate scaling factors are selected,the local adap-tive activation functions not only improve the convergence rate of PINNs models,but also obtain higher precision numerical solutions while maintaining computational efficiency.关键词
Burgers-Fisher方程/物理信息神经网络/自适应激活函数/偏微分方程求解Key words
Burgers-Fisher equation/physics-informed neural networks/adaptive activation functions/partial differential equation solving分类
信息技术与安全科学引用本文复制引用
孙宇,朱海龙..局部自适应物理信息神经网络在求解Burgers-Fisher方程中的应用[J].山东理工大学学报（自然科学版）,2025,39(4):47-53,7.基金项目
安徽省科研编制计划重点项目(2024AH050013) （2024AH050013）
