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Article

A Deep Learning Framework for Parameter Estimation in 1D Marine Ecosystem Model

by
Ao Li
1,†,
Kewei Zhao
2,†,
Weiwei Fang
2,
Chan Shu
3,*,
Runjie Zhou
4,
Qiuyi Li
5,
Xiaolong Huang
6,
Xiaohong Lei
1,
Menghan Xu
3,
Haoyu Jiang
7 and
Lin Mu
7
1
College of Marine Science and Technology, China University of Geosciences, Wuhan 430074, China
2
State Key Laboratory of Marine Environmental Science, College of Ocean and Earth Sciences, Xiamen University, Xiamen 361000, China
3
College of Mathematics and Statistics, Huanggang Normal University, Huanggang 438000, China
4
Department of Weaponary Engineering, Naval University of Engineering, Wuhan 430033, China
5
College of Information Engineering, Hefei Binhu Vocational and Technical College, Hefei 230601, China
6
Eco-Environmental Monitoring and Research Center, Pearl River Valley and South China Sea Ecology and Environment Administration, Ministry of Ecology and Environment, Guangzhou 510611, China
7
College of Life Sciences and Oceanography, Shenzhen University, Shenzhen 518055, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
J. Mar. Sci. Eng. 2025, 13(7), 1228; https://doi.org/10.3390/jmse13071228
Submission received: 9 April 2025 / Revised: 15 June 2025 / Accepted: 24 June 2025 / Published: 26 June 2025
(This article belongs to the Special Issue Machine Learning Methodologies and Ocean Science)
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Abstract

Marine ecosystems play an increasingly critical role in both global climate regulation and the impacts of anthropogenic activities. Accurate marine biogeochemical numerical models are essential tools for understanding and predicting the complex dynamics of these systems. However, as model complexity increases, so does the number of biological parameters and the uncertainties associated with them, which can substantially affect model performance. Consequently, efficient and reliable parameter estimation has become a key challenge in model development and application. In this study, we proposed a deep learning-based approach for parameter estimation in numerical models, utilizing deep neural networks to capture the complex nonlinear relationships between numerical model input parameters and output variables. A one-dimensional marine ecosystem model is employed as a case study to evaluate the effectiveness of the proposed method. The results demonstrate that (1) the deep learning approach provides an automated and adaptive solution for parameter estimation, significantly improving the efficiency of model calibration in engineering and scientific applications by enabling rapid identification of near-optimal parameter sets; and (2) the deep learning model effectively learns the underlying nonlinear mappings between inputs and outputs. During training, the mean squared error (MSE) loss exhibits a steady decline, with minor fluctuations in the early stages, ultimately converging to a stable value. The predicted parameter combinations show strong agreement with the reference numerical model outputs, yielding correlation coefficients exceeding 0.95.
Keywords: deep learning; neural networks; numerical modeling; parameter estimation deep learning; neural networks; numerical modeling; parameter estimation

Share and Cite

MDPI and ACS Style

Li, A.; Zhao, K.; Fang, W.; Shu, C.; Zhou, R.; Li, Q.; Huang, X.; Lei, X.; Xu, M.; Jiang, H.; et al. A Deep Learning Framework for Parameter Estimation in 1D Marine Ecosystem Model. J. Mar. Sci. Eng. 2025, 13, 1228. https://doi.org/10.3390/jmse13071228

AMA Style

Li A, Zhao K, Fang W, Shu C, Zhou R, Li Q, Huang X, Lei X, Xu M, Jiang H, et al. A Deep Learning Framework for Parameter Estimation in 1D Marine Ecosystem Model. Journal of Marine Science and Engineering. 2025; 13(7):1228. https://doi.org/10.3390/jmse13071228

Chicago/Turabian Style

Li, Ao, Kewei Zhao, Weiwei Fang, Chan Shu, Runjie Zhou, Qiuyi Li, Xiaolong Huang, Xiaohong Lei, Menghan Xu, Haoyu Jiang, and et al. 2025. "A Deep Learning Framework for Parameter Estimation in 1D Marine Ecosystem Model" Journal of Marine Science and Engineering 13, no. 7: 1228. https://doi.org/10.3390/jmse13071228

APA Style

Li, A., Zhao, K., Fang, W., Shu, C., Zhou, R., Li, Q., Huang, X., Lei, X., Xu, M., Jiang, H., & Mu, L. (2025). A Deep Learning Framework for Parameter Estimation in 1D Marine Ecosystem Model. Journal of Marine Science and Engineering, 13(7), 1228. https://doi.org/10.3390/jmse13071228

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