Physics-Guided Graph Convolutional Deep Equilibrium Network for Environmental Data

TL;DR: This study proposes a physics-guided graph convolutional deep equilibrium network for environmental data modeling, incorporating physical laws into a graph-based DEQ model, and demonstrates improved performance in air quality estimation tasks using real-world data.

Abstract: Modelling environmental data, including temperature and air pollution, has been tackled by both physical methods and deep learning models. The former approach builds upon physical laws albeit using computationally complex algorithms. Alternatively, deep learning methods are purely data-driven, exploiting diverse spatiotemporal data correlations. While the latter delivers good performance and fast inference, it does not leverage knowledge about the physical phenomena. Recently, deep equilibrium networks (DEQs), i.e., networks that find the fixed point of some iterative procedure, have shown outstanding performance when compared with their equivalent deep models. In this work, we propose a physics-guided DEQ model for environmental data that can be modeled as a graph. Our approach builds on a graph convolutional operator, incorporating the partial differential equation that defines the convection-diffusion physical process. We evaluate the effectiveness of our approach in the task of air quality estimation based on sensor measurements. Experiments on real-world air quality data show the improved performance of our model with respect to state-of-the-art approaches.