Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen

TL;DR

This paper introduces a physics-informed neural network framework with a collocation-based approach for simulating pollution spread under thermal inversion conditions, validated by a case study in Spitsbergen.

Contribution

It develops a mathematically grounded, robust loss function and a collocation strategy for efficient training of neural networks in time-dependent pollution modeling.

Findings

Thermal inversion significantly increases particulate matter concentration near the ground.

The proposed neural network framework accurately captures pollution dynamics under inversion conditions.

Field measurements support the model's predictions of pollutant trapping and accumulation.

Abstract

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.