**ClimODE: Climate and Weather Forecasting with Physics-Informed Neural ODEs** **Authors:** Yogesh Verma, Markus Heinonen, Vikas Garg **Institution:** Aalto University, Finland; YaiYai Ltd **Abstract:** ClimODE is a novel approach to climate and weather forecasting that leverages physics-informed neural ordinary differential equations (ODEs). It addresses the limitations of traditional numerical simulations and data-driven models by incorporating physical principles, specifically advection, into its architecture. ClimODE models precise weather evolution with value-conserving dynamics, enabling global and regional forecasting with improved uncertainty quantification. The model outperforms existing methods in terms of accuracy and computational efficiency, demonstrating state-of-the-art performance in global and regional forecasting tasks. **Key Contributions:** 1. **Model Architecture:** ClimODE implements a continuous-time, second-order neural continuity equation, ensuring value-conserving dynamics and stable long-horizon forecasts. 2. **Flow Velocity Network:** It integrates local convolutions, long-range attention, and a Gaussian emission network to capture both local and global effects. 3. **Uncertainty Estimation:** The model addresses the issue of uncertainty in predictions by incorporating an emission model that accounts for aleatoric and epistemic variance. 4. **Performance:** ClimODE achieves superior performance in global and regional forecasting tasks, outperforming competitive methods in metrics such as RMSE and ACC. **Methods:** - **Continuity Equation:** The model is based on the advection equation, which describes the movement of weather quantities over time and space. - **Flow Velocity Network:** A hybrid network combines convolutional and attention mechanisms to capture both local and global effects. - **Spatio-Temporal Embedding:** Trigonometric and spherical-position encodings are used to encode daily, seasonal, and spatial periodicities. - **Initial Velocity Inference:** An optimized initial velocity is estimated using penalized least-squares to ensure accurate ODE solutions. - **Loss Function:** The model minimizes the negative log-likelihood of observations, incorporating both mean and variance predictions. **Experiments:** - **Global and Regional Forecasting:** ClimODE is evaluated on various meteorological variables, showing superior performance compared to other methods. - **Climate Forecasting:** It demonstrates effective monthly average forecasting, outperforming competitors in key meteorological variables. - **Ablation Studies:** The impact of individual components on the model's performance is analyzed, highlighting the importance of each component. **Conclusion:** ClimODE provides a physics-informed approach to climate and weather forecasting, offering accurate predictions and uncertainty quantification. Its effectiveness in various forecasting tasks underscores its potential for practical applications in weather and climate modeling.**ClimODE: Climate and Weather Forecasting with Physics-Informed Neural ODEs** **Authors:** Yogesh Verma, Markus Heinonen, Vikas Garg **Institution:** Aalto University, Finland; YaiYai Ltd **Abstract:** ClimODE is a novel approach to climate and weather forecasting that leverages physics-informed neural ordinary differential equations (ODEs). It addresses the limitations of traditional numerical simulations and data-driven models by incorporating physical principles, specifically advection, into its architecture. ClimODE models precise weather evolution with value-conserving dynamics, enabling global and regional forecasting with improved uncertainty quantification. The model outperforms existing methods in terms of accuracy and computational efficiency, demonstrating state-of-the-art performance in global and regional forecasting tasks. **Key Contributions:** 1. **Model Architecture:** ClimODE implements a continuous-time, second-order neural continuity equation, ensuring value-conserving dynamics and stable long-horizon forecasts. 2. **Flow Velocity Network:** It integrates local convolutions, long-range attention, and a Gaussian emission network to capture both local and global effects. 3. **Uncertainty Estimation:** The model addresses the issue of uncertainty in predictions by incorporating an emission model that accounts for aleatoric and epistemic variance. 4. **Performance:** ClimODE achieves superior performance in global and regional forecasting tasks, outperforming competitive methods in metrics such as RMSE and ACC. **Methods:** - **Continuity Equation:** The model is based on the advection equation, which describes the movement of weather quantities over time and space. - **Flow Velocity Network:** A hybrid network combines convolutional and attention mechanisms to capture both local and global effects. - **Spatio-Temporal Embedding:** Trigonometric and spherical-position encodings are used to encode daily, seasonal, and spatial periodicities. - **Initial Velocity Inference:** An optimized initial velocity is estimated using penalized least-squares to ensure accurate ODE solutions. - **Loss Function:** The model minimizes the negative log-likelihood of observations, incorporating both mean and variance predictions. **Experiments:** - **Global and Regional Forecasting:** ClimODE is evaluated on various meteorological variables, showing superior performance compared to other methods. - **Climate Forecasting:** It demonstrates effective monthly average forecasting, outperforming competitors in key meteorological variables. - **Ablation Studies:** The impact of individual components on the model's performance is analyzed, highlighting the importance of each component. **Conclusion:** ClimODE provides a physics-informed approach to climate and weather forecasting, offering accurate predictions and uncertainty quantification. Its effectiveness in various forecasting tasks underscores its potential for practical applications in weather and climate modeling.