Spatiotemporal diffusion with Koopman operator for multistep prediction of short-term time-series

Multistep time-series prediction of a high-dimensional system presents a persistent challenge across scientific domains, particularly with short-term data. Drawing inspiration from Takens’ embedding theorem, the existing spatiotemporal information (STI) transformation framework transforms the spatial/association information of multiple variables into the temporal dynamics of a target variable, thereby achieving promising results on short-term high-dimensional sequence prediction. However, traditional STI transformation functions are constructed using regression, which does not consider the latent prior properties of complex nonstationary scenarios, resulting in the accumulation of errors or underutilization of historical data, thereby degrading performance in several cases. In this study, we propose a spatiotemporal diffusion (STD) framework using the Koopman operator to achieve an interpretable, accurate multistep prediction of short-term time series. One key feature of the proposed STD framework is its embedding of dynamic system knowledge and specific task knowledge in STI function approximation and target variable prediction. Validations across diverse short-term high-dimensional datasets and refinement experiments highlight the STD model’s robustness and efficiency.