Graph grammars and Physics Informed Neural Networks for simulating of pollution propagation on Spitzbergen

In this paper, we present two computational methods for performing simulations of pollution propagation described by advection-diffusion equations. The first method employs graph grammars to describe the generation process of the computational mesh used in simulations with the meshless solver of the three-dimensional finite element method. The graph transformation rules express the three-dimensional Rivara longest-edge refinement algorithm. This solver is used for an exemplary application: performing three-dimensional simulations of pollution generation by the recently closed coal-burning power plant and the new diesel power plant, the capital of Spitzbergen. The second computational code is based on the Physics Informed Neural Networks method. It is used to calculate the dissipation of the pollution along the valley in which the city of Longyearbyen is located. We discuss the instantiation and execution of the PINN method using Google Colab implementation. There are four novelties of our paper. First, we show a lower computational cost of the proposed graph grammar model in comparison with the mesh transformations over the computational mesh. Second, we discuss the benefits and limitations of the PINN implementation of the non-stationary advection-diffusion model with respect to finite element method solvers. Third, we introduce the PINN code for non-stationary thermal inversion simulations. Fourth, using our computer simulations, we estimate the influence of the pollution from power plants on the Spitzbergen inhabitants.