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Fourier Amplitude and Correlation Loss: Beyond Using L2 Loss for Skillful Precipitation Nowcasting
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Proposes Fourier Amplitude and Correlation Loss (FACL), an alternating FAL/FCL loss replacing MSE for spatiotemporal precipitation nowcasting, plus a new Regional Histogram Divergence metric.
Problem
Deep precipitation nowcasting models trained with pixel-wise L2 losses (MSE) produce blurry predictions with limited operational utility, while generative alternatives are slow and non-deterministic.
Approach
Replace MSE with a parameter-free Fourier loss that alternates between a Fourier Amplitude Loss (sharpness) and a Fourier Correlation Loss (structure), with alternation probability shifting toward FAL over training, plus a sigmoid output layer; also proposes RHD, a histogram-based patch metric tolerant to local shifts.
Key results
- On Stochastic Moving-MNIST, FACL reduces LPIPS by up to 57% and RHD by up to 71% for ConvLSTM relative to MSE.
- On SEVIR, FACL improves ConvLSTM FVD from 510.2 to 289.5 and FSS from 0.5252 to 0.5640 while MAE rises slightly from 26.35 to 27.60 (x10^-3).
- On HKO-7, FACL improves SimVP LPIPS from 0.3039 to 0.2912 and FVD from 808.1 to 555.1, while MAE is slightly worse (30.93 to 31.65).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace MSE with FACL | ConvLSTM · Stochastic Moving-MNIST | LPIPS: 0.2538 -> 0.1092 | Helped |
| Replace MSE with FACL | ConvLSTM · Stochastic Moving-MNIST | FSS: 0.6148 -> 0.8172 | Helped |
| Replace MSE with FACL | ConvLSTM · Stochastic Moving-MNIST | MAE: 196.4 -> 180.1 | Helped |
| Replace MSE with FACL | ConvLSTM · SEVIR | LPIPS: 0.3683 -> 0.3508 | Helped |
| Replace MSE with FACL | ConvLSTM · SEVIR | CSI-m: 0.3957 -> 0.3984 | Helped |
| Replace MSE with FACL | ConvLSTM · MeteoNet | LPIPS: 0.1504 -> 0.1252 | Helped |
| Replace MSE with FACL | ConvLSTM · HKO-7 | FSS: 0.2653 -> 0.4045 | Helped |
| Add Fourier Correlation Loss to FAL (ablation) | ConvLSTM with FAL · Stochastic Moving-MNIST | LPIPS: 0.5854 -> 0.1092 | Helped |
| Add Fourier Amplitude Loss to FCL (ablation) | ConvLSTM with FCL · Stochastic Moving-MNIST | LPIPS: 0.2102 -> 0.1092 | Helped |
| Set α to 0.2 instead of 0.0 (ablation) | PredRNN with FACL · Stochastic Moving-MNIST | LPIPS: 0.0997 -> 0.0806 | Helped |
| Set α to 0.3 instead of 0.0 (ablation) | ConvLSTM with FACL · SEVIR | LPIPS: 0.3502 -> 0.3312 | Helped |
Surprising findings
- FAL alone yields meaningless outputs (MSE 302.7, FSS 0.0019 on Stochastic Moving-MNIST), showing the correlation term is required.
- On N-body-MNIST, MSE-trained models match or beat FACL, so FACL gains do not hold on the deterministic dataset.
Limitations
- Assumes monotonic radar echo data and may not generalize to multi-modal datasets.
- No regularization on temporal consistency, which may misalign features across frames.
- Pixel-wise metrics (MAE, SSIM, MSE) degrade slightly with FACL.
Experimental setup
Datasets: Stochastic Moving-MNIST N-body-MNIST SEVIR MeteoNet HKO-7
Benchmarks: Stochastic Moving-MNIST N-body-MNIST SEVIR MeteoNet HKO-7
Metrics: MAE SSIM LPIPS FVD FSS RHD CSI pooled CSI
Baselines: MSE LDCast MCVD PreDiff STRPM
Builds on: ConvLSTM PredRNN SimVP Earthformer Focal Frequency Loss
Closest papers by meaning
- PostCast: Generalizable Postprocessing for Precipitation Nowcasting via Unsupervised Blurriness Modeling (ICLR 2025 · similarity 0.87)
- Perceptually Constrained Precipitation Nowcasting Model (ICML 2025 · similarity 0.86)
- AlphaPre: Amplitude-Phase Disentanglement Model for Precipitation Nowcasting (CVPR 2025 · similarity 0.86)
- Data-driven Precipitation Nowcasting Using Satellite Imagery (AAAI 2025 · similarity 0.85)
- FourierMamba: Fourier Learning Integration with State Space Models for Image Deraining (ICML 2025 · similarity 0.85)
- DiffCast: A Unified Framework via Residual Diffusion for Precipitation Nowcasting (CVPR 2024 · similarity 0.85)
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