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ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs
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Proposes ClimODE, a physics-informed neural ODE model implementing a second-order neural advection (continuity) equation with a Gaussian emission model, for global, regional and monthly weather/climate forecasting on ERA5.
Problem
Deep learning weather forecasters are black-box, ignore underlying atmospheric physics, are not value-conserving over long horizons, and lack uncertainty quantification.
Approach
Model weather as a continuous-time advection (continuity) PDE over the Earth, learned as a system of neural ODEs with a second-order flow velocity network combining local convolutions and global attention, plus a probabilistic emission model that adds bias and variance to capture sources and uncertainty.
Key results
- ClimODE with about 2.8M parameters reports lower latitude-weighted RMSE than ClimaX, FourCastNet and NODE on most global variables and lead times, e.g. z at 6h RMSE 102.9 vs FCN 149.4.
- In regional forecasting, ClimODE achieves the lowest RMSE for t2m, t and z across North America, South America and Australia, while remaining competitive on u10 and v10.
- ClimODE falls short of the IFS gold standard, as expected, on the variables where IFS is reported.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ClimODE instead of FourCastNet | Global ERA5 forecasting · z, 6 hours | RMSE: 149.4 -> 102.9 ± 9.3 | Helped |
| Use ClimODE instead of FourCastNet | Global ERA5 forecasting · t2m, 6 hours | RMSE: 1.28 -> 1.21 ± 0.09 | Helped |
| Use ClimODE instead of FourCastNet | Global ERA5 forecasting · u10, 6 hours | RMSE: 1.47 -> 1.41 ± 0.07 | Helped |
| Add the advection ODE form (ablation) | Second-order neural ODE for weather forecasting · ERA5 forecasting | unweighted RMSE | Helped |
| Add global attention to convolutions (ablation) | Advection ODE for weather forecasting · ERA5 forecasting | unweighted RMSE | Helped |
| Add the emission model (ablation) | Advection ODE with global attention · ERA5 forecasting | unweighted RMSE | Helped |
Surprising findings
- Wind components (u10, v10) are where ClimODE is least competitive; ClimaX or FCN are better at some regional wind lead times.
Limitations
- Uses only five ERA5 variables at coarse 5.625 degree resolution and does not use pre-training or many variables.
- Falls short of the IFS physics simulator on global forecasts.
- Unclear whether the model can forecast reliably under climate change, as stated in the conclusion.
Experimental setup
Datasets: ERA5 WeatherBench
Benchmarks: WeatherBench ERA5 global forecasting regional forecasting (North America, South America, Australia) monthly climate forecasting
Metrics: latitude-weighted RMSE ACC CRPS
Baselines: NODE ClimaX FourCastNet IFS
Builds on: neural ODE ClimaX FourCastNet WeatherBench
Closest papers by meaning
- ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Prediction (NeurIPS 2024 · similarity 0.86)
- OmniCast: A Masked Latent Diffusion Model for Weather Forecasting Across Time Scales (NeurIPS 2025 · similarity 0.85)
- DiffDA: a Diffusion model for weather-scale Data Assimilation (ICML 2024 · similarity 0.85)
- Probablistic Emulation of a Global Climate Model with Spherical DYffusion (NeurIPS 2024 · similarity 0.84)
- Tyche: One Step Flow for Efficient Probabilistic Weather Forecasting (NeurIPS 2026 · similarity 0.84)
- CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs (NeurIPS 2025 · similarity 0.84)
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