The Cross-twin Physics-informed Neural Network for Wave Equations with Conserved Quantities

Li Jianhao; Fang Jinwei

doi:10.12052/gdutxb.240152

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The Cross-twin Physics-informed Neural Network for Wave Equations with Conserved Quantities

更新时间：2026-05-27

- The Cross-twin Physics-informed Neural Network for Wave Equations with Conserved Quantities
- Vol. 43, Issue 2, Pages: 41-51(2026)
- 作者机构：
  
  广东工业大学数学与统计学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.240152
  CLC： TP183
- Published：2026
- 稿件说明：
移动端阅览
李剑豪, 房金伟. 具守恒量波动方程的循环双子网物理信息神经网络[J]. 广东工业大学学报, 2026, 43(2): 41-51.
李剑豪, 房金伟. 具守恒量波动方程的循环双子网物理信息神经网络[J]. 广东工业大学学报, 2026, 43(2): 41-51. DOI： 10.12052/gdutxb.240152.

DOI： 10.12052/gdutxb.240152

摘要

物理信息神经网络(Physics-Informed Neural Networks

PINNs)在求解偏微分方程(Partial Differential Equations

PDEs)及复杂物理系统建模中展现出较大潜力。然而，其在处理多尺度、多区域场景以及多物理耦合系统时，存在训练效率低、优化不稳定等问题。本文在现有PINNs方法基础上，针对波动方程，提出了一种基于守恒量的循环双子网络(Cross-Twin Network

CTN)求解方法。该方法通过引入交互式信息共享与约束机制，显著提升了模型在多区域、多尺度场景下的收敛速度、预测精度与训练稳定性。实验结果表明，与传统方法相比，循环双子网络在非线性高阶波动偏微分方程和方程组的求解中表现优异。本文为PINNs的研究与应用提供了新的思路。

Abstract

Physics-Informed Neural Networks (PINNs) have demonstrated significant potential in solving partial differential equations (PDEs) and modeling complex physical systems. However

when dealing with multi-scale

multi-domain scenarios and multi-physics coupled systems

PINNs face challenges such as low training efficiency and optimization instability. Based on existing PINN methods

a conservation-based Cross-Twin Network (CTN) approach is proposed for solving wave equations. By introducing interactive information-sharing and constraint mechanisms

the proposed method significantly improves the convergence speed

prediction accuracy

and training stability in multi-domain and multi-scale scenarios. Experimental results show that

compared with traditional methods

the Cross-Twin Network achieves superior performance in solving nonlinear higher-order wave PDEs and equation systems. This study provides new insights for the research and application of PINNs.

关键词

Keywords

references

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