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FNP: Fourier Neural Processes for Arbitrary-Resolution Data Assimilation
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Proposes Fourier Neural Processes (FNP), a neural-process model with SetConv embedding, neural Fourier layers, and dynamic alignment-and-merge, enabling data assimilation of observations at arbitrary resolutions without interpolation.
Problem
AI-based data assimilation methods only handle observations at the same resolution as the forecast model, so observations must be interpolated, introducing errors and limiting generalization to other resolutions.
Approach
Uses a neural process conditioned on background and observation coordinate-value sets, with SetConv embedding, spatial-variable decoupled representations, neural Fourier layers for high-frequency detail, and a similarity-based dynamic alignment and merge module to fuse background and observation features at the target resolution.
Key results
- At 0.25° observation resolution, FNP without fine-tuning reaches MSE 0.0196 vs 0.0288 background, and fine-tuned FNP reaches MSE 0.0058 (best) with RMSE reductions over 50% on v10, u500, v500, q700 relative to 1.40625° results.
- At 1.40625° resolution with 10% observations, FNP achieves MSE 0.0202 vs Adas 0.0221 and ConvCNP 0.0252.
- On observational information reconstruction (no background), fine-tuned FNP achieves MSE 0.0291 vs ConvCNP 0.0350 and Adas 0.0370.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FNP instead of Adas | ERA5 data assimilation with 1.40625° observations · 1.40625° observations | MSE: 0.0221 -> 0.0202 | Helped |
| Use FNP instead of Adas | ERA5 data assimilation with 0.703125° observations · 0.703125° observations | MSE: 0.0144 -> 0.0085 | Helped |
| Use FNP instead of Adas | ERA5 data assimilation with 0.25° observations · 0.25° observations | MSE: 0.0231 -> 0.0058 | Helped |
| Fine-tune FNP for observational information reconstruction | FNP · ERA5 observational information reconstruction, 10% observations | MSE: 0.0355 -> 0.0291 | Helped |
| Add neural Fourier layers instead of standard CNN layers (ablation) | FNP · ERA5 data assimilation, 1.40625° observations | MSE: 0.0230 -> 0.0202 | Helped |
| Add dynamic alignment and merge (DAM) (ablation) | FNP · ERA5 data assimilation, 1.40625° observations | MSE: 0.0214 -> 0.0202 | Helped |
| Add spatial-variable decoupled (SVD) representation (ablation) | FNP · ERA5 data assimilation, 1.40625° observations | MSE: 0.0239 -> 0.0202 | Helped |
| Increase observation resolution from 1.40625° to 0.703125° | FNP · ERA5 data assimilation | MSE: 0.0202 -> 0.0085 | Helped |
| Increase observation resolution from 0.703125° to 0.25° | FNP · ERA5 data assimilation | MSE: 0.0085 -> 0.0058 | Helped |
Surprising findings
- Adas, fine-tuned on interpolated observations, gets worse at 0.25° resolution than at 0.703125°, indicating interpolation information loss outweighs the benefit of more observations.
- Without fine-tuning, FNP at 0.25° resolution still improves over the background in MSE, showing out-of-distribution resolution generalization.
Limitations
- Observations are simulated from ERA5 by masking rather than real-world observations.
- Performs 3D assimilation without a temporal dimension.
- Adas and other baselines are not flexible to arbitrary resolutions, so comparisons require interpolation or fine-tuning choices.
Experimental setup
Datasets: ERA5
Benchmarks: ERA5
Metrics: MSE MAE latitude-weighted RMSE
Baselines: Adas ConvCNP background (no assimilation)
Builds on: neural processes ConvCNP Fourier neural operator SetConv
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