Application of physics-informed neural networks in solving temperature diffusion equation of seawater

Lei HAN; Changming DONG; Yuli LIU; Huarong XIE; Hongchun ZHANG; Weijun ZHU

doi:10.1007/s00343-025-4348-1

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Application of physics-informed neural networks in solving temperature diffusion equation of seawater

Physics | Updated：2026-03-26

- Application of physics-informed neural networks in solving temperature diffusion equation of seawater
- Application of physics-informed neural networks in solving temperature diffusion equation of seawater
- 海洋湖沼学报(英文) 2026年44卷第1期页码：1-18
- Affiliations：
  
  1.School of Atmospheric Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China
  2.School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China
  3.Southern Ocean Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, China
  4.School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China
- Author bio：
  
  cmdong@nuist.edu.cn
- Funds：
  
  the National Key Research and Development Program of China(2023YFC3008200);the Independent Research Project of Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai)(SML2022SP505)
- DOI：10.1007/s00343-025-4348-1
  中图分类号：
- 收稿：2024-12-18，
  
  录用：2025-01-24，
  
  网络首发：2025-03-21，
  
  纸质出版：2026-01-01
- Accepted：
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Lei HAN, Changming DONG, Yuli LIU, 等. Application of physics-informed neural networks in solving temperature diffusion equation of seawater[J]. 海洋湖沼学报(英文), 2026,44(1):1-18.

HAN Lei,DONG Changming,LIU Yuli,et al.Application of physics-informed neural networks in solving temperature diffusion equation of seawater[J].Journal of Oceanology and Limnology,2026,44(01):1-18.
Lei HAN, Changming DONG, Yuli LIU, 等. Application of physics-informed neural networks in solving temperature diffusion equation of seawater[J]. 海洋湖沼学报(英文), 2026,44(1):1-18. DOI： 10.1007/s00343-025-4348-1.

HAN Lei,DONG Changming,LIU Yuli,et al.Application of physics-informed neural networks in solving temperature diffusion equation of seawater[J].Journal of Oceanology and Limnology,2026,44(01):1-18. DOI： 10.1007/s00343-025-4348-1.

摘要

Abstract

Physics-informed neural networks (PINNs)

as a novel artificial intelligence method for solving partial differential equations

are applicable to solve both forward and inverse problems. This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios

including forward and inverse problems under three different boundary conditions. Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems. Inaccurate weighting of terms in the loss function can reduce model accuracy. Additionally

the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions. In particular

the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems. In contrast

for the Neumann and Robin boundary conditions

accuracy declines when points were sampled from identical positions or at the same time. Subsequently

the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean. The PINNs successfully captured the vertical diffusion characteristics of seawater temperature

reflected the seasonal changes of vertical temperature under different topographic conditions

and revealed the influence of topography on the temperature diffusion coefficient. The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data

providing a promising technique for simulating or predicting ocean phenomena using sparse observations.

关键词

Keywords

references

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