Collaborative Imputation of Urban Time Series through Cross-city Meta-learning

—Urban time series, such as mobility flows, energy consumption, and pollution records, encapsulate complex urban dynamics and structures. However, data collection in each city is impeded by technical challenges such as budget limitations and sensor failures, necessitating effective data imputation techniques that can enhance data quality and reliability. Existing imputation models, categorized into learning-based and analytics-based paradigms, grapple with the trade-off between capacity and generalizability. Collaborative learning to reconstruct data across multiple cities holds the promise of breaking this trade-off. Nevertheless, urban data’s inherent irregularity and heterogeneity issues exacerbate challenges of knowledge sharing and collaboration across cities. To address these limitations, we propose a novel collaborative imputation paradigm leveraging meta-learned implicit neural representations (INRs). INRs offer a continuous mapping from domain coordinates to target values, integrating the strengths of both paradigms. By imposing embedding theory, we first employ continuous parameterization to handle irregularity and reconstruct the dynamical system. We then introduce a cross-city collaborative learning scheme through model-agnostic meta learning, incorporating hierarchical modulation and normalization techniques to accommodate multiscale representations and reduce variance in response to heterogeneity. Extensive experiments on a diverse urban dataset from 20 global cities demonstrate our model’s superior imputation performance and generalizability, underscoring the effectiveness of collaborative imputation in resource-constrained settings.