Physics-informed cross-coupled information flow modeling for spatiotemporal dynamical systems

Modeling complex spatiotemporal dynamical systems with strong non-stationarity and underlying physical constraints remains a fundamental challenge. While deep learning approaches have shown promising performance, they often lack physical consistency and interpretability. In this work, we propose a unified physics-informed spatiotemporal learning framework that formulates system evolution as a structured information flow process. Specifically, we embed convection–diffusion dynamics into recurrent state transitions, enabling physically grounded information propagation through learnable operators. Building upon this formulation, we introduce a cross-coupled recurrent mechanism that explicitly models bidirectional interactions across hierarchical representations, thereby enhancing the modeling of complex spatiotemporal dependencies. Furthermore, an adaptive multi-scale interaction scheme is incorporated to dynamically regulate information flow across spatial regions and feature channels, improving representation expressiveness under non-stationary conditions. A physics-informed constraint further regularizes the learned dynamics toward physically consistent evolution patterns. Extensive experiments on real-world wind field datasets demonstrate that the proposed framework consistently outperforms state-of-the-art methods, achieving an RMSE of 1.85 m/s and an MAE of 1.21 m/s. The model also demonstrates strong spatial generalization and temporal extrapolation capability. In addition, the proposed model requires 86.8% fewer parameters, 67.8% lower computational cost, and achieves 28.6% faster inference, demonstrating its practical applicability for real-world deployment. These results suggest that explicitly modeling physics-constrained information flow provides a principled and effective paradigm for spatiotemporal dynamical system learning.