广东工业大学 数学与统计学院,广东,广州,510520
李剑豪(1999–) ,男,硕士研究生,主要研究方向为偏微分方程数值解,E-mail:1023594343@qq.com
房金伟(1987–) ,男,讲师,博士,主要研究方向为偏微分方程数值解,E-mail:fangjinwei@gdut.edu.cn
纸质出版:2026
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.
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.
RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. [J]. Journal Computer Physics, 2019, 378: 686-707.
RAO C, SUN H, LIU Y. Physics-informed deep learning for incompressible laminar flows[J]. Theoretical and Applied Mechanics Letters, 2020, 10(3): 207-212.
JAGTAP A D, KHARAZMI E, KARNIADAKIS G E. Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 365: 113028.
MENG X, LI Z, ZHANG D, et al . PPINN: parareal physics-informed neural network for time-dependent PDEs[J ] . Computer Methods in Applied Mechanics and Engineering, 2020, 370: 113250.
GAO H, SUN L, WANG J X. PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain[J]. Journal of Computational Physics, 2021, 428: 110079.
DENG S C, SONG X T, ZHONG M X, et al . A dynamic balanced physics-informed neural network for solving partial differential equations[J ] . Scientia Sinica Informationis, 2024, 54(8): 1843-1859.
PSAROS A F, KAWAGUCHI K, KARNIADAKIS G E. Meta-learning PINN loss functions[J]. Journal of computational physics, 2022, 458: 111121.
LU L, PESTOURIE R, YAO W, et al . Physics-informed neural networks with hard constraints for inverse design[J ] . SIAM Journal on Scientific Computing, 2021, 43(6): B1105-B1132.
MENG X, KARNIADAKIS G E. A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems[J]. Journal of Computational Physics, 2020, 401: 109020.
LIN S N, CHEN Y. A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions [J]. Journal of Computational Physics, 2022(10): 111053.
JUNCAI P, WEIQI P, YONG C. The data-driven localized wave solutions of the derivative nonlinear Schrödinger equation by using improved PINN approach [J]. Wave Motion, 2021(11): 102823.
HAGHIGHAT E, RAISSI M, MOURE A, et al . A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics[J ] . Computer Methods in Applied Mechanics and Engineering, 2021, 379: 113741.
YUAN L, NI Y Q, DENG X Y, et al . A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations[J ] . Journal of Computational Physics, 2022, 462: 111260.
0
浏览量
0
下载量
0
CSCD
关联资源
相关文章
相关作者
相关机构
京公网安备11010802024621