具守恒量波动方程的循环双子网物理信息神经网络OA
The Cross-twin Physics-informed Neural Network for Wave Equations with Conserved Quantities
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.
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.
李剑豪;房金伟
广东工业大学 数学与统计学院,广东 广州 510520广东工业大学 数学与统计学院,广东 广州 510520
信息技术与安全科学
物理信息神经网络偏微分方程波动方程循环双子网络守恒律
physics-informed neural networkpartial differential equationswave equationcross-twin networkconservation laws
《广东工业大学学报》 2026 (2)
41-51,11
国家自然科学基金青年基金资助项目(12001115)广州市科技计划项目(202201010648)
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