Koopman theory meets graph convolutional network: Learning the complex dynamics of non-stationary highway traffic flow for spatiotemporal prediction

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Reliable and accurate traffic flow prediction is crucial for the construction and operation of smart highways, supporting scientific traffic management and planning. However, accurately predicting spatiotemporal traffic flow in non-stationary and unprecedented traffic patterns scenarios, such as holidays and adverse weather conditions, remains a challenging task. Considering that (1) Koopman theory effectively captures the underlying time-variant dynamics of the non-stationary temporal sequence (2) Graph convolutional network (GCN) effectively extracts complex spatial dependencies, combining the strengths of both is a promising solution. Therefore, this paper proposes a spatiotemporal prediction network that integrates Koopman theory and GCN, named KoopGCN, for predicting non-stationary and inexperienced highway traffic flow. KoopGCN decomposes the input into time-invariant and time-variant components based on Fast Fourier Transform. The dual engine block consisting of KoopGCN InvarEngine and KoopGCN VarEngine is designed to predict two types of components separately. And the dual engine block also passes the residual to the next block for modeling. The experiment is conducted on real monitored highway data in Ningde City, Fujian Province, China. The results indicate that even if there is a significant distribution difference between the training and testing sets, KoopGCN can achieve accurate prediction, significantly outperforms state-of-the-art baselines.