Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen
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 als...
| Authors | Maciej Sikora, Leszek Siwik, Natalia Leszczyńska et al. |
|---|---|
| Primary category | cs.LG |
| Published | 24 April 2026 |
| Last updated at source | 22 August 2026 |
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