PDED: Revitalize physics laws submerged in data information for Traffic State Estimation

Yao Fu, Hong Zhao, Xiaoyu Cai, Ruiheng Yang, Weihao Jiang, Shiliang Pu

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: Physics-informed deep learning, Traffic state estimation, Knowledge distillation, Ensemble learning

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Abstract: Traditional physics-informed deep learning combines the data-driven methods with the model-based methods by incorporating physics loss as a constraint in total loss function in general, which aims to enforce the neural network to behave according to the physics property. However, this simple integration makes physical knowledge submerged in data information since data loss and physics loss could have large magnitude differences, conflicting directions of the gradients, and varying convergence rates so that the physics law may not work as expected and inhibits the model from working effectively furthermore, especially for traffic state estimation (TSE). To alleviate these issues, we propose a Physical knowledge combined Data information neural network with Ensemble Distillation framework (PDED) to first disentangle the data-driven model and physics-based model, and then reassemble them to take advantages of label information and physics property. Practically, we separately train data-driven model based on true labels and physics-based model according to physics laws. Then, we introduce the ensemble learning and knowledge distillation to assemble their representations of these two models for constructing a more competitive learnable online teacher model, which in turn distills knowledge to guide the update of them for learning richer knowledge to improve the performance of student models. Through extensive experiments on both synthetic dataset and real-world datasets, our model demonstrates better performance than the existing state-of-the-art methods.

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Submission Number: 3151