In this paper, we propose a Physics-Informed Neural Network framework for time-dependent simulations of pollution propagation originating from moving emission sources. We formulate a robust variational framework for the time-dependent advection-diffusion problem and establish the boundedness and inf-sup stability of the corresponding discrete weak formulation. Based on this mathematical foundation, we construct a robust loss function that is directly related to the true approximation error, defined as the difference between the neural network approximation and the (unknown) exact solution. Additionally, a collocation-based strategy is introduced to speed up neural network training. As a case study, we investigate pollution propagation caused by snowmobile traffic in Longyearbyen, Spitsbergen, supported by detailed in-field measurements collected using dedicated sensors. The proposed framework is applied to analyze the effects of thermal inversion on pollutant accumulation. Our results demonstrate that thermal inversion traps dense and humid air masses near the ground, significantly enhancing particulate matter (PM) concentration and worsening local air quality.

翻译：本文提出了一种物理信息神经网络框架，用于模拟移动排放源引发的污染物传播时变过程。针对时变平流-扩散问题，我们构建了鲁棒变分框架，并建立了相应离散弱形式的有界性与inf-sup稳定性。基于这一数学基础，我们构建了与真实逼近误差（即神经网络逼近与未知精确解之差）直接相关的鲁棒损失函数。此外，引入了一种基于配置点的策略以加速神经网络训练。以斯匹次卑尔根岛朗伊尔城的雪地摩托交通引发的污染传播为案例研究，我们利用专用传感器采集的详细现场测量数据进行了验证。该框架被应用于分析逆温对污染物累积的影响，结果表明逆温会将稠密潮湿气团困于近地面，显著增加颗粒物浓度并恶化局部空气质量。