Multi-Frequency Graph Neural Rough Differential Equations for Traffic Forecasting

Abstract The burgeoning field of neural differential equations (NDEs) underscores a quest for models that not only boast interpretability and robustness but also function within a more generalized framework. Although the fusion of Neural Controlled Differential Equations (NCDEs) with Graph Neural Networks (GNNs) has marked significant strides in traffic forecasting, the prolonged integrative process requisite for long-term forecasts remains a detriment to model efficacy. Furthermore, while NCDEs exhibit prowess in extracting temporal trends within traffic fluctuations, the potential of spatial trend correlations has not been adequately investigated. To bridge this gap, we introduce the Multi-Frequency Graph Neural Rough Differential Equation (MFG-NRDE), an NDE-based model tailored for traffic forecasting. Our model is underpinned by the frequency principle in neural networks and leverages both wavelet and signature transforms. This dual approach not only truncates the integral length but also captures a more nuanced representation of high- and low-frequency temporal features. Complementing this temporal focus, we integrate a novel methodology for dynamically computing spatial correlations, harnessing the inherent trend characteristics of traffic variations to enhance spatial dimension analysis. Empirical validation across four real-world traffic flow datasets demonstrates the superior performance of our MFG-NRDE model, positioning it favorably against contemporary state-of-the-art baselines. This underscores the efficacy of our model in managing the intricate dynamics of traffic data forecasting, paving the way for more sophisticated and accurate predictive models in this domain.