Physical Informed Neural Networks for modeling ocean pollutant

2025/07/07 by Battina, Karishma, Joshi, Prathamesh Dinesh, Dandekar, Raj Abhijit +2
#FOS: Computer and information sciences #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2507.08834

Abstract

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

Citations

• Long-term simulation of physical and mechanical behaviors using curriculum-transfer-learning based physics-informed neural networks
• Physics Informed Neural Networks with strong and weak residuals for advection-dominated diffusion problems
• Neural tangent kernel analysis of PINN for advection-diffusion equation
• Physics-informed machine learning
• When and why PINNs fail to train: A neural tangent kernel perspective
• When and why PINNs fail to train: A neural tangent kernel perspective
• Universal Differential Equations for Scientific Machine Learning
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Julia: A Fresh Approach to Numerical Computing
• Julia: A Fresh Approach to Numerical Computing

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• Application of Physics-Informed Neural Networks for Solving the Inverse Advection-Diffusion Problem to Localize Pollution Sources
• Physics-informed neural networks in water and wastewater systems: a critical review
• Representing ill-known parts of a numerical model using a machine learning approach