用物理约束神经网络模拟海洋污染物扩散，提升复杂环境下的预测精度。
Physical Informed Neural Networks for modeling ocean pollutant
- 将二维对流-扩散方程嵌入神经网络，通过物理定律约束模型输出
- 在含噪合成数据上训练，实现边界与初值条件的精确满足
- 基于Julia生态实现高效可扩展，适合动态海洋污染场景建模
传统数值方法在大规模动态海洋域中模拟污染物传输时面临复杂性与规模挑战。本文提出一种物理信息神经网络（PINN）框架，用于求解由二维对流-扩散方程描述的污染物扩散问题。模型通过将物理规律及初始/边界条件直接嵌入神经网络训练过程，结合噪声合成数据（由有限差分法生成）进行拟合，实现物理一致的预测。该方法有效应对非线性动力学及边值条件施加难题。合成数据集引入不同噪声水平以模拟真实世界变异性。训练采用混合损失函数，包含偏微分方程残差、边界/初始条件符合度及加权数据拟合项。利用Julia语言科学计算生态，实现高性能仿真，为传统求解器提供可扩展、灵活的替代方案。
原文摘要 · Abstract (English)
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
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