福州大学学报（自然科学版）2024，Vol.52Issue(4)：396-403,8.DOI:10.7631/issn.1000-2243.23166
基于改进欧拉法的非线性偏微分方程神经网络求解器
Neural network solver for nonlinear partial differential equations based on improved Euler method
摘要
Abstract
To address the poor generalization performance of conventional deep learning methods in solving nonlinear partial differential equations,a long short-term convolutional recurrent neural network with an improved Euler method connected network module is proposed.The construction of the neural network employs the improved Euler method and finite difference method.Effective connections between the modules are realized through the improved Euler method.The derivative terms involved in the partial differential equation are accurately approximated by convolutions kernels constructed based on the finite difference method.Simulation experiments are conducted on two typical nonlinear partial differential equations,namely the Burgers equation and λ-ω reaction-diffusion equation.The experi-mental results prove that this method not only has high precision on the training data,but also shows strong generalization ability when extrapolating to new fields.关键词
偏微分方程/深度学习/长短期记忆/改进欧拉法/有限差分法Key words
partial differential equations/deep learning/long short-term memory/improved Euler method/finite difference method分类
数理科学引用本文复制引用
黄冠男,王靖岳,王美清..基于改进欧拉法的非线性偏微分方程神经网络求解器[J].福州大学学报（自然科学版）,2024,52(4):396-403,8.基金项目
国家自然科学基金资助项目(62172098) （62172098）
