Eco-PiNN: A Physics-informed Neural Network for Eco-toll Estimation

The eco-toll estimation problem quantifies the expected environmental cost (e.g., energy consumption, exhaust emissions) for a vehicle to travel along a path. This problem is important for societal applications such as eco-routing, which aims to find paths with the lowest exhaust emissions or energy need. The challenges of this problem are three-fold: (1) the dependence of a vehicle's eco-toll on its physical parameters; (2) the lack of access to data with eco-toll information; and (3) the influence of contextual information (i.e. the connections of adjacent segments in the path) on the eco-toll of road segments. Prior work on eco-toll estimation has mostly relied on pure data-driven approaches and has high estimation errors given the limited training data. To address these limitations, we propose a novel Eco-toll estimation Physics-informed Neural Network framework (Eco-PiNN) using three novel ideas, namely, (1) a physics-informed decoder that integrates the physical laws of the vehicle engine into the network, (2) an attention-based contextual information encoder, and (3) a physics-informed regularization to reduce overfitting. Experiments on real-world heavy-duty truck data show that the proposed method can greatly improve the accuracy of eco-toll estimation compared with state-of-the-art methods.