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

A team of ten researchers from AGH University of Krakow, University of Oslo, and other institutions has developed a Physics-Informed Neural Network (PINN) framework for simulating pollution propagation from moving emission sources under complex atmospheric conditions. Their paper, submitted to arXiv on April 24, 2026, focuses on the advection-diffusion problem and introduces a robust variational formulation that ensures boundedness and inf-sup stability of the discrete weak form. This mathematical foundation allows them to construct a loss function directly tied to the true approximation error, improving accuracy over traditional PINNs. They also employ a collocation-based strategy to accelerate neural network training, making the approach practical for real-world simulations.

The case study examines pollution from snowmobile traffic in Longyearbyen, Spitsbergen, using detailed in-field measurements from dedicated sensors. The framework reveals that thermal inversion conditions—where a layer of warm air traps cooler, denser air near the ground—significantly enhance particulate matter (PM) concentration. This trapping effect worsens local air quality, highlighting the risks of Arctic tourism and transportation. The open-source software and methodology offer a new tool for environmental monitoring in cold regions, with potential applications in urban air quality management and climate impact studies.