Modeling Pollution Spread with Obstructions using Physics-Informed Neural Networks

Pollution modeling plays a crucial role in combating climate change and protecting public health. Scientists rely on traditional numerical methods, such as finite difference and computational fluid dynamics, for accurate pollution simulations; however, they are resource-intensive and time-consuming often taking days to execute. Physics-Informed Neural Networks (PINNs) present a promising alternative, capable of significantly improving speed while maintaining high accuracy. In our research, we developed a PINN to model pollution spread under laminar flow conditions in a two-dimensional environment with obstructions and reflecting boundaries. Our model integrates the Navier-Stokes and advection-diffusion partial differential equations (PDEs) and enforces zero-flux Neumann boundaries at obstruction surfaces and simulation edges. We used a hybrid learning approach, generating a dataset of 6.1 million colocation points for supervised learning and embedding physical laws into the loss function for unsupervised learning. In our experiments, the PINN was over 2520 times faster than the traditional numerical solver, returning results in under 2190 milliseconds and achieving a mean squared error below 3E-5. Our findings demonstrate that PINNs not only offer a drastic reduction in computational time but also scale favorably with both the time domain and spatial resolution, making them a viable solution for real-time pollution monitoring and emergency response planning. Future work will focus on extending our model to dynamic obstructions and arbitrary grid geometries.