Algorithms 2026, 19(7), 577; https://doi.org/10.3390/a19070577 (registering DOI) - 14 Jul 2026
Abstract
To address the high non-stationarity of COVID-19 pandemic time-series data and the severe error accumulation issue in long-horizon forecasting, a spatiotemporal two-branch multi-step forecasting model named CFC-FLCA is proposed. This model integrates closed-form continuous-time neural networks (CFC), a hybrid decomposition strategy combining variational
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To address the high non-stationarity of COVID-19 pandemic time-series data and the severe error accumulation issue in long-horizon forecasting, a spatiotemporal two-branch multi-step forecasting model named CFC-FLCA is proposed. This model integrates closed-form continuous-time neural networks (CFC), a hybrid decomposition strategy combining variational mode decomposition (VMD) and jump plus AM-FM mode decomposition (JMD), and a cross-attention (CA) mechanism. First, the VMD-JMD hybrid mode decomposition method is applied to preprocess raw new case sequences. By leveraging the complementary advantages of the two decomposition algorithms, non-stationary sequences are adaptively decomposed into high-frequency noise components and low-to-mid-frequency trend-periodic components, eliminating random disturbance interference at the data source. On this basis, a time–frequency dual-branch feature extraction network is constructed. CFC provides ultra-long-range temporal dependency modeling capability; the time-domain branch adopts Legendre projection units (LPU) to extract robust temporal evolution features, while the frequency-domain branch employs frequency-enhanced units (FEU) to uncover latent periodic patterns that are difficult to capture using traditional time-domain methods. A cross-attention mechanism is introduced to dynamically learn the importance weights of time–frequency-domain features, enabling the adaptive deep integration of complementary information and effectively mitigating error accumulation in long-horizon forecasting. Multi-step forecasting experiments are conducted on real-world COVID-19 datasets from Belgium, the Czech Republic, and Ireland, with comprehensive comparisons against mainstream time series forecasting models. The experimental results demonstrate that the CFC-FLCA model outperforms all comparison models across all evaluation metrics for all prediction horizons.
Full article
(This article belongs to the Topic Theoretical Foundations and Applications of Deep Learning Techniques)
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