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

Maciej Sikora; Leszek Siwik; Natalia Leszczyńska; Tomasz Maciej Ciesielski; Eirik Valseth; Manuela Bastidas Olivares; Marcin Łoś; Tomasz Służalec; Jacek Leszczyński; Maciej Paszyński

arXiv · 2604.23003

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

Maciej Sikora·Leszek Siwik·Natalia Leszczyńska·Tomasz Maciej Ciesielski·Eirik Valseth·Manuela Bastidas Olivares·Marcin Łoś·Tomasz Służalec·Jacek Leszczyński·Maciej Paszyński

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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. We also extend our model to the non-linear Burgers-type equations. 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. We compare our method to linear computational cost explicit dynamics solver using isogeometric analysis. We show that our method can solve non-linear non-stationary problem four times slower than IGA solver can solve the linear problem. It makes it particularly interesting to investigate the non-linear extensions with similar computational cost as the linear formulation.

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Maciej Sikora, Leszek Siwik, Natalia Leszczyńska, Tomasz Maciej Ciesielski, Eirik Valseth, Manuela Bastidas Olivares, Marcin Łoś, Tomasz Służalec, Jacek Leszczyński, Maciej Paszyński. 2026-04-24. Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen. https://arxiv.org/abs/2604.23003

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