中国物理B ›› 2026, Vol. 35 ›› Issue (4): 40202-040202.doi: 10.1088/1674-1056/ae030b

• • 上一篇    下一篇

Modified PINN approach integrating conservation laws for efficient multi-stage training of coupled nonlinear systems

Jie Deng(邓婕) and Lijia Han(韩励佳)†   

  1. Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
  • 收稿日期:2025-07-21 修回日期:2025-08-25 接受日期:2025-09-04 发布日期:2026-04-01
  • 通讯作者: Lijia Han E-mail:hljmath@ncepu.edu.cn
  • 基金资助:
    Lijia Han is supported in part by the National Natural Science Foundation of China (Grant No. 11971166).

Modified PINN approach integrating conservation laws for efficient multi-stage training of coupled nonlinear systems

Jie Deng(邓婕) and Lijia Han(韩励佳)†   

  1. Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
  • Received:2025-07-21 Revised:2025-08-25 Accepted:2025-09-04 Published:2026-04-01
  • Contact: Lijia Han E-mail:hljmath@ncepu.edu.cn
  • Supported by:
    Lijia Han is supported in part by the National Natural Science Foundation of China (Grant No. 11971166).

PDF (PC)

5

赞

摘要： We propose an innovative conservation multi-stage algorithm (CM) based on physics-informed neural networks (PINNs) to investigate the dynamics of vector solitons governed by Zakharov equation. By ingeniously integrating conservation laws into the multi-stage training algorithm, we enhanced the method's constraint and physical consistency in solving nonlinear systems. Numerical simulations of the Zakharov and nonlinear Schrödinger (NLS) equations demonstrated that our method showed obvious improvements in approximation accuracy, convergence speed, and training efficiency, compared to traditional PINN methods. Moreover, when the parameter representing the speed of sound is sufficiently large, our method efficiently simulates the approximation from the Zakharov equation to the NLS equation. The approximative simulation not only confirms the conservation multi-stage algorithm's applicability in various physical environments but also highlights its potential in controlling sound wave propagation characteristics to simulate NLS equation behavior.

关键词: physics-informed neural network, Zakharov equation, nonlinear Schrödinger equation, limit behavior

Abstract: We propose an innovative conservation multi-stage algorithm (CM) based on physics-informed neural networks (PINNs) to investigate the dynamics of vector solitons governed by Zakharov equation. By ingeniously integrating conservation laws into the multi-stage training algorithm, we enhanced the method's constraint and physical consistency in solving nonlinear systems. Numerical simulations of the Zakharov and nonlinear Schrödinger (NLS) equations demonstrated that our method showed obvious improvements in approximation accuracy, convergence speed, and training efficiency, compared to traditional PINN methods. Moreover, when the parameter representing the speed of sound is sufficiently large, our method efficiently simulates the approximation from the Zakharov equation to the NLS equation. The approximative simulation not only confirms the conservation multi-stage algorithm's applicability in various physical environments but also highlights its potential in controlling sound wave propagation characteristics to simulate NLS equation behavior.

Key words: physics-informed neural network, Zakharov equation, nonlinear Schrödinger equation, limit behavior

中图分类号:  (Numerical approximation and analysis)

  • 02.60.-x
52.35.-g (Waves, oscillations, and instabilities in plasmas and intense beams) 02.30.Jr (Partial differential equations) 02.60.Cb (Numerical simulation; solution of equations)