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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2604.21058 |
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| _version_ | 1866910158833057792 |
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| author | Ilyas, Muhammad |
| author_facet | Ilyas, Muhammad |
| contents | Predicting nutrient transport and salinity distribution is crucial for mitigating climate-related threats to agromaritime systems. Traditional PDE-based models can capture the physics of nutrient dispersion, salinity and water quality. However, they face challenges in scalability and adaptability to real-time problems. In this article, we develop a hybrid approach that combines finite element discretisations with neural network integration to enable efficient and adaptive data-informed predictions. We use a finite element solver for the steady-state diffusion-reaction equation to generate a dataset across varying diffusivity, reaction and inflow conditions. We then build a proper orthogonal decomposition (POD), which reduces dimensionality, and a neural network (NN) that maps parameters to reduced coefficients. A numerical study presented on a simplified model demonstrates the proof-of-concept for predicting nutrient transport and salinity distribution. Numerical experiments show that the NN surrogate achieve a speed-up of approximately 956x compared to a regular FEM solver while maintaining an accuracy of mean relative L2-errors of 15% across the test set, with occasional higher deviations, which is sufficient for rapid scenario screening and parametric studies. These results highlight the method's potential as a fast and accurate surrogate for nutrient and salinity prediction, offering a balance between FEM reliability and NN adaptability for sustainable agromaritime management. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21058 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-Driven Surrogate Models for Agromaritime Applications: Finite Element-Neural Network Integration Ilyas, Muhammad Numerical Analysis 65N30 Predicting nutrient transport and salinity distribution is crucial for mitigating climate-related threats to agromaritime systems. Traditional PDE-based models can capture the physics of nutrient dispersion, salinity and water quality. However, they face challenges in scalability and adaptability to real-time problems. In this article, we develop a hybrid approach that combines finite element discretisations with neural network integration to enable efficient and adaptive data-informed predictions. We use a finite element solver for the steady-state diffusion-reaction equation to generate a dataset across varying diffusivity, reaction and inflow conditions. We then build a proper orthogonal decomposition (POD), which reduces dimensionality, and a neural network (NN) that maps parameters to reduced coefficients. A numerical study presented on a simplified model demonstrates the proof-of-concept for predicting nutrient transport and salinity distribution. Numerical experiments show that the NN surrogate achieve a speed-up of approximately 956x compared to a regular FEM solver while maintaining an accuracy of mean relative L2-errors of 15% across the test set, with occasional higher deviations, which is sufficient for rapid scenario screening and parametric studies. These results highlight the method's potential as a fast and accurate surrogate for nutrient and salinity prediction, offering a balance between FEM reliability and NN adaptability for sustainable agromaritime management. |
| title | Data-Driven Surrogate Models for Agromaritime Applications: Finite Element-Neural Network Integration |
| topic | Numerical Analysis 65N30 |
| url | https://arxiv.org/abs/2604.21058 |