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<p>Accurate surface temperature forecasting is a critical necessity for adaptation and risk management amid intensifying climate change and extreme weather events. While deep learning methods have shown significant potential in this domain, current deep learning models for physical forecasting are often constrained by inadequate representation of intrinsic data properties, reliance on static spatial dependencies, and a lack of deeply-integrated physical constraints. To address these limitations, this study introduces Geometric-Convolutional ODE with Dynamic Spectral modeling (GCODS), a novel hybrid framework, which synergistically integrates a Hybrid Geometric-Convolutional Encoder (HGCE) to enhance input physical fidelity, with a hybrid continuous-time dynamics solver. Its core is the Moore-constrained Continuous Dynamics Parameterization Network (MCDP-Net), which provides a generalizable, PDE-based modeling approach combining state-adaptivity and dynamic topology to learn the spatio-temporal evolution of physical operators. This design allows the physically informed, state-adaptive dynamics to model local processes, while the global residual corrections, driven by a spectral module, capture large-scale atmospheric phenomena. Evaluated on the WeatherBench dataset, GCODS quantitatively outperforms existing baselines, achieving a global 6-h forecast latitude-weighted Root Mean Square Error (RMSE) of 0.92&#xa0;K and an Anomaly Correlation Coefficient (ACC) of 0.99, alongside a 144-h RMSE of 2.52&#xa0;K and an ACC of 0.91. Furthermore, diagnostic experiments confirm its ability to generate physically plausible forecasts of complex phenomena, simulating the 2017–2018 Southeast Australia heatwave and capturing the large-scale patterns of the 2017–2018 La Niña teleconnection. This work provides a structured framework for integrating learnable, state-adaptive physical operators into data-driven models for computational physics modeling.</p>

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GCODS: A hybrid geometric-convolutional ode framework with dynamic spectral modeling for surface temperature forecasting

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月25日

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  • Yucong Lu,
  • Xinyue Mo,
  • Huan Li

摘要

Accurate surface temperature forecasting is a critical necessity for adaptation and risk management amid intensifying climate change and extreme weather events. While deep learning methods have shown significant potential in this domain, current deep learning models for physical forecasting are often constrained by inadequate representation of intrinsic data properties, reliance on static spatial dependencies, and a lack of deeply-integrated physical constraints. To address these limitations, this study introduces Geometric-Convolutional ODE with Dynamic Spectral modeling (GCODS), a novel hybrid framework, which synergistically integrates a Hybrid Geometric-Convolutional Encoder (HGCE) to enhance input physical fidelity, with a hybrid continuous-time dynamics solver. Its core is the Moore-constrained Continuous Dynamics Parameterization Network (MCDP-Net), which provides a generalizable, PDE-based modeling approach combining state-adaptivity and dynamic topology to learn the spatio-temporal evolution of physical operators. This design allows the physically informed, state-adaptive dynamics to model local processes, while the global residual corrections, driven by a spectral module, capture large-scale atmospheric phenomena. Evaluated on the WeatherBench dataset, GCODS quantitatively outperforms existing baselines, achieving a global 6-h forecast latitude-weighted Root Mean Square Error (RMSE) of 0.92 K and an Anomaly Correlation Coefficient (ACC) of 0.99, alongside a 144-h RMSE of 2.52 K and an ACC of 0.91. Furthermore, diagnostic experiments confirm its ability to generate physically plausible forecasts of complex phenomena, simulating the 2017–2018 Southeast Australia heatwave and capturing the large-scale patterns of the 2017–2018 La Niña teleconnection. This work provides a structured framework for integrating learnable, state-adaptive physical operators into data-driven models for computational physics modeling.