ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs

TL;DR

ClimODE introduces a continuous-time, physics-informed neural advection model for climate and weather forecasting that enforces mass-conserving dynamics while quantifying uncertainty. It learns a neural transport velocity using a hybrid local Convolution and global Attention architecture, augmented by a Gaussian emission model for sources and variability. Across global, regional, and climate-scale tasks on ERA5/WeatherBench data, ClimODE achieves state-of-the-art results with substantially fewer parameters than transformer-based rivals and provides calibrated uncertainty estimates. Ablation studies confirm the critical role of advection and emission components in driving performance, while mass conservation is empirically validated over long horizons.

Abstract

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts. However, they often act as data-driven black-box models that neglect the underlying physics and lack uncertainty quantification. We address these limitations with ClimODE, a spatiotemporal continuous-time process that implements a key principle of advection from statistical mechanics, namely, weather changes due to a spatial movement of quantities over time. ClimODE models precise weather evolution with value-conserving dynamics, learning global weather transport as a neural flow, which also enables estimating the uncertainty in predictions. Our approach outperforms existing data-driven methods in global and regional forecasting with an order of magnitude smaller parameterization, establishing a new state of the art.

Figures (14)

• Figure 1: Weather as a quantity-preserving advection system. A quantity (eg. temperature) (a) is moved by a neural flow velocity (b), whose divergence is the flow's compressibility (c). The flow translates into state change by advection (d), which combine quantity's transport (e) and compression (f).
• Figure 2: Conceptual illustration of continuity equation on pointwise temperature change$\dot{u}(\mathbf{x}_0,t) = - \mathbf{v} \cdot \nabla u - u\nabla \cdot \mathbf{v}$. (a) A perpendicular flow (green) to the gradient (bluetored) moves in equally hot air causing no change at $\mathbf{x}_0$. (b) Cool air moves upwards, decreasing pointwise temperature, while air concentration at $\mathbf{x}_0$ accumulates additional temperature. (c) Hot air moves downwards increasing temperature at $\mathbf{x}_0$, while air dispersal decreases it.
• Figure 3: Whole prediction pipeline for ClimODE.
• Figure 4: $\mathrm{RMSE} (\downarrow)$ and $\mathrm{ACC} (\uparrow)$ comparison with baselines. ClimODE outperforms competitive neural methods across different metrics and variables. For more details, see Table \ref{['tab:bench_table']}.
• Figure 5: CRPS and Monthly Forecasting: $\mathrm{RMSE} (\downarrow)$ comparison with FourCastNet (FCN) for monthly forecasting and $\mathrm{CRPS}$ scores for ClimODE.