Physics-Informed Neural Network Super Resolution for Advection-Diffusion Models

Physics-informed neural networks (NN) are an emerging technique to improve spatial resolution and enforce physical consistency of data from physics models or satellite observations. A super-resolution (SR) technique is explored to reconstruct high-resolution images ($4\times$) from lower resolution images in an advection-diffusion model of atmospheric pollution plumes. SR performance is generally increased when the advection-diffusion equation constrains the NN in addition to conventional pixel-based constraints. The ability of SR techniques to also reconstruct missing data is investigated by randomly removing image pixels from the simulations and allowing the system to learn the content of missing data. Improvements in S/N of $11\%$ are demonstrated when physics equations are included in SR with $40\%$ pixel loss. Physics-informed NNs accurately reconstruct corrupted images and generate better results compared to the standard SR approaches.