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This research advances Physics-Informed Neural Networks (PINNs) by introducing a collocation-based strategy to accelerate training for complex, time-dependent advection-diffusion problems. The study validates the framework using real-world data from Spitsbergen, demonstrating its ability to model pollution dynamics under specific thermal inversion conditions with rigorous mathematical stability guarantees. While the current implementation shows slower performance compared to linear isogeometric analysis solvers, the approach offers a promising pathway for handling non-linear environmental simulations where traditional methods face computational bottlenecks.
Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen
arXiv:2604.23003v2 Announce Type: replace 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.
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.
Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE)
G.1.8; G.4; I.6.7; I.2.m
arXiv:2604.23003 [cs.LG]
(or arXiv:2604.23003v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2604.23003 Focus to learn more arXiv-issued DOI via DataCite
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