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

Yan Li, Mingzhou Yang, Matthew J Eagon, Majid Farhadloo, Yiqun Xie, William F. Northrop, Shashi Shekhar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


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 threefold: (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 governing vehicle dynamics 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.

Original languageEnglish (US)
Title of host publication2023 SIAM International Conference on Data Mining, SDM 2023
PublisherSociety for Industrial and Applied Mathematics Publications
Number of pages9
ISBN (Electronic)9781611977653
StatePublished - 2023
Event2023 SIAM International Conference on Data Mining, SDM 2023 - Minneapolis, United States
Duration: Apr 27 2023Apr 29 2023

Publication series

Name2023 SIAM International Conference on Data Mining, SDM 2023


Conference2023 SIAM International Conference on Data Mining, SDM 2023
Country/TerritoryUnited States

Bibliographical note

Publisher Copyright:
Copyright © 2023 by SIAM.


  • eco-toll estimation
  • physics-informed machine learning
  • spatiotemporal data mining


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