# Physical Informed Neural Networks for modeling ocean pollutant

arXiv: https://arxiv.org/abs/2507.08834 · HTML: https://mlsanity.com/paper/2507.08834/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 7 of 7)

- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Long-term simulation of physical and mechanical behaviors using curriculum-transfer-learning based physics-informed neural networks](https://mlsanity.com/paper/2502.07325/) (2025)
- [Neural tangent kernel analysis of PINN for advection-diffusion equation](https://mlsanity.com/paper/2211.11716/) (2022)

## Abstract (arXiv)

Traditional numerical methods often struggle with the complexity and scale of modeling pollutant transport across vast and dynamic oceanic domains. This paper introduces a Physics-Informed Neural Network (PINN) framework to simulate the dispersion of pollutants governed by the 2D advection-diffusion equation. The model achieves physically consistent predictions by embedding physical laws and fitting to noisy synthetic data, generated via a finite difference method (FDM), directly into the neural network training process. This approach addresses challenges such as non-linear dynamics and the enforcement of boundary and initial conditions. Synthetic data sets, augmented with varying noise levels, are used to capture real-world variability. The training incorporates a hybrid loss function including PDE residuals, boundary/initial condition conformity, and a weighted data fit term. The approach takes advantage of the Julia language scientific computing ecosystem for high-performance simulations, offering a scalable and flexible alternative to traditional solvers