A Physics-Regularized Multiscale Attention Network for Spatiotemporal Traffic Data Imputation

Spatiotemporal traffic data imputation is a fundamental task in numerous smart mobility applications. Existing studies indicate that accurately estimating missing values from observed data relies on capturing the spatiotemporal dependencies in traffic data. However, such dependencies may exhibit distinct characteristics across varying spatiotemporal areas, such as local short-term traffic fluctuations versus global long-range periodic commuting patterns. The comprehensive multiscale nature of dependencies in traffic data, encompassing more than just local and global levels, has not been well explored in the literature. To address this issue, we propose a physics-regularized multiscale attention network (PRMAN) that hierarchically extracts spatiotemporal features from local dynamics to global trends. Specifically, the proposed PRMAN builds upon the novel Swin Transformer and introduces a hierarchical architecture that performs self-attention in local spatiotemporal windows. By systematically expanding the window size across layers, this hierarchical design explicitly addresses the distinct characteristics between local and global spatiotemporal dependencies at different scales. Meanwhile, a physics-regularized loss function is developed to align learned spatiotemporal dependencies with traffic dynamics described by the fundamental diagram. This improves the model’s generalizability beyond the training data, ensuring robust performance on unseen datasets. Numerical experiments on multiple benchmark datasets demonstrate that our proposed PRMAN achieves state-of-the-art performance in handling diverse and complex missing data patterns. The code and model are publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/2222ad/PRMAN</uri>