求解Burger方程的自适应神经网络方法分析  

Analysis of Adaptive Neural Network Methods for Solving the Burger's Equation

作　　者：李晓磊 LI Xiaolei(School of Computer Science and Technology,University of Science and Technology of China,Anhui 230027,China)

机构地区：[1]中国科学技术大学计算机科学与技术学院,安徽230027

出　　处：《电子技术（上海）》2024年第4期68-71,共4页Electronic Technology

摘　　要：阐述一种求解偏微分方程的自适应深度学习方法。传统数值解法,如有限元法和有限积分法,由于需要对可行域进行网格划分,存在维数灾难等问题。基于深度学习的物理信息神经网络(PINN)用于求解偏微分方程的方法,则存在精度和训练效率等方面的挑战。为此,介绍一种自适应物理信息神经网络(AdaPINN)的方法,该方法结合自适应激活函数和损失函数权重自适应策略。实验结果表明,AdaPINN在Burger方程的求解精度和训练效率方面具有一定的改善效果。This paper describes an adaptive deep learning method for solving partial differential equations.Traditional numerical methods,such as finite element method and finite integral method,suffer from the curse of dimensionality due to the need for mesh partitioning of feasible regions.Methods based on Physics-Informed Neural Networks(PINN) for solving partial differential equations face challenges in terms of accuracy and training efficiency.This paper presents a method called Adaptive Physics-Informed Neural Network(AdaPINN),which combines adaptive activation functions and a loss function weight adaptation strategy.Experimental results demonstrate that AdaPINN exhibits improvements in both the accuracy and training efficiency of solving the Burger equation.

关 键 词：科学计算 深度学习 自适应物理信息神经网络 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] TP391.41[自动化与计算机技术—控制科学与工程]