四川大学学报（自然科学版）2024，Vol.61Issue(5)：69-79,11.DOI:10.19907/j.0490-6756.2024.052005
基于有限差分残差物理约束的波动方程无监督学习方法
Unsupervised learning method for the wave equation based on finite difference residual constraints loss
摘要
Abstract
The wave equation is an important physical partial differential equation,and in recent years,deep learning has shown potential to accelerate or replace traditional numerical methods for solving it.However,existing deep learning methods suffer from high data acquisition costs,low training efficiency,and insufficient generalization capability for boundary conditions.To address these issues,this paper proposes an unsuper-vised learning method for the wave equation based on finite difference residual constraints.The authors con-struct a novel finite difference residual constraint based on structured grids and finite difference methods,as well as an unsupervised training strategy,enabling convolutional neural networks to train without data and predict the forward propagation process of waves.Experimental results demonstrate that finite difference re-sidual constraints have advantages over Physics-Informed Neural Networks(PINNs)type physical informa-tion constraints,such as easier fitting,lower computational costs,and stronger source term generalization ca-pability,making our method more efficient in training and potent in application.关键词
卷积神经网络/有限差分方法/波动方程/无监督学习Key words
Convolutional Neural Network/Finite difference method/Wave equation/Unsupervised learning分类
信息技术与安全科学引用本文复制引用
冯鑫,姜屹,秦嘉贤,张来平,邓小刚..基于有限差分残差物理约束的波动方程无监督学习方法[J].四川大学学报（自然科学版）,2024,61(5):69-79,11.基金项目
国家重大专项(GJXM92579) （GJXM92579）
基础科研计划(JCKY2022110C119) （JCKY2022110C119）
