基于PINN模型求解一维和二维STO方程  

Solving the One-and-Two Dimensional STO Equations Based on the PINN Method

作　　者：王晶[1] 戴厚平[1] 董亚茹 WANG Jing;DAI Houping;DONG Yaru(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000

出　　处：《吉首大学学报(自然科学版)》2025年第1期18-24,共7页Journal of Jishou University(Natural Sciences Edition)

基　　金：湖南省教育厅科学研究重点项目(21A0329);湖南省自然科学基金资助项目(2021JJ30548)。

摘　　要：利用物理信息神经网络(PINN)模型求解一维和二维Sharam-Tasso-Olver方程.将宏观方程及其初边值条件作为物理信息并转化为残差形式,再利用残差构造损失函数融入PINN模型的训练过程中,利用Adam优化算法实现高精度求解.数值算例结果表明,损失函数在一定的迭代次数下有较高的精度,这验证了STO方程的PINN模型求解的有效性.Physically informed neural networks(PINN)model are used to solve the one-and two-dimensional Sharam-Tasso-Olver equations.The macroscopic equations and their initial margin conditions are used as physical information and transformed into the form of residuals,which are then used to construct a loss function to incorporate into the training process of the PINN model,and the Adam optimisation algorithm is used to achieve a high-precision solution.The numerical example results show that the loss function has high accuracy under a certain number of iterations,which verifies the reliability of the PINN model.

关 键 词：神经网络 物理信息神经网络 Sharam-Tasso-Olver方程 

分 类 号：O241.82[理学—计算数学]