基于PINN模型求解一维和二维STO方程

doi:10.13438/j.cnki.jdzk.2025.01.003

吉首大学学报（自然科学版） ›› 2025, Vol. 46 ›› Issue (1): 18-24.DOI: 10.13438/j.cnki.jdzk.2025.01.003

基于PINN模型求解一维和二维STO方程

王晶，戴厚平，董亚茹

(吉首大学数学与统计学院,湖南吉首 416000)

出版日期:2025-01-01 发布日期:2025-01-20
作者简介:王晶(1998—)，女，山东临沂人，吉首大学数学与统计学院硕士研究生，主要从事微分方程数值解研究
基金资助:
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)

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

WANG Jing,DAI Houping,DONG Yaru

(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

Online:2025-01-01 Published:2025-01-20

摘要/Abstract

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到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STIO方程的PINN模型的求解有效性.

关键词： 神经网络, 物理信息神经网络, Sharam-Tasso-Olver方程

Abstract: 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.

Key words: neural networks, physically informed neural network, Sharam-Tasso-Olver equation

王晶, 戴厚平, 董亚茹. 基于PINN模型求解一维和二维STO方程[J]. 吉首大学学报（自然科学版）, 2025, 46(1): 18-24.

WANG Jing, DAI Houping, DONG Yaru. Solving the One-and-Two Dimensional STO Equations Based on the PINN Method[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(1): 18-24.

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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

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