Combining Physics and Machine Learning for Network Flow Estimation

The flow estimation problem consists of predicting missing edge flows in a network (e.g., traffic, power and water) based on partial observations. These missing flows depend both on the underlying physics (edge features and a flow conservation law) as well as the observed edge flows. This paper introduces an optimization framework for computing missing flows and solves the problem using bilevel optimization and deep learning. Empirical results show that the method accurately predicts missing flows, outperforming the best baseline by up to 20%, and is able to capture relevant physical properties in traffic and power networks.