AdaptFNO: Adaptive Fourier Neural Operator with Dynamic Spectral Modes and Multiscale Learning for Climate Modeling

Authors:
Hiep Vo Dang (Yeshiva University), Bach D. G. Nguyen (Michigan State University), Phong C. H. Nguyen (Phenikaa University), Truong-Son Hy (University of Alabama at Birmingham) - Correspondence to [email protected]

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📖 Overview

Fourier Neural Operators (FNOs) are powerful for modeling spatio-temporal dynamics but often emphasize low-frequency patterns, overlooking fine-scale details critical in climate forecasting.
We introduce AdaptFNO, an adaptive variant that:

• Dynamically adjusts spectral modes based on input frequency content.
• Combines global and local operators for multiscale learning.
• Uses a cross-attention mechanism to align global and local features.

AdaptFNO effectively captures both large-scale circulation and fine-grained events such as typhoon trajectories, with efficient long-range stability.

This codebase accompanies our NeurIPS 2025 Workshop paper:

"AdaptFNO: Adaptive Fourier Neural Operator with Dynamic Spectral Modes and Multiscale Learning for Climate Modeling".

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📐 Architecture

The figure below illustrates the overall architecture of AdaptFNO:

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✨ Features

• Dynamic spectral mode allocation to handle both low- and high-frequency structures.
• Multiscale design:
  • Global operator (low-res, large-scale patterns)
  • Local operator (high-res, fine details)
• Cross-attention mechanism for efficient knowledge transfer from global to local forecasts.
• Validated on ERA5 reanalysis data with case studies (e.g., Typhoon Yagi).

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📂 Repository Structure

AdaptFNO-main/
│
├── models/              # AdaptFNO, FNO, and baseline model definitions
├── data/                # Scripts for downloading and preprocessing ERA5 data
├── training/            # Training loop, loss functions, and optimization setup
├── utils/               # Helper functions (metrics, visualization, etc.)
├── experiments/         # Example experiment configurations
├── figures/             # Plots of results (e.g., Typhoon Yagi trajectory)
└── main.py              # Entry point for training and evaluation

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⚙️ Installation

Clone the repository and install dependencies:

git clone https://github.com/HySonLab/AdaptFNO.git
cd AdaptFNO
pip install -r requirements.txt

Recommended environment:

• Python 3.9+
• PyTorch 2.0+
• CUDA 11.8+ (for GPU training)

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📊 Dataset

We use the ERA5 reanalysis dataset (hourly data on pressure levels 250, 500, 850 hPa).

• Download from Copernicus Climate Data Store.
• Preprocessing scripts are provided in data/.

Variables included:

• U/V wind components
• Vertical velocity
• Temperature
• Relative humidity
• Geopotential

Data is split chronologically:

• Training: 1980–2022
• Validation: 2023–2024

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🚀 Usage

Training

Run the following to train AdaptFNO:

python main.py --config configs/adaptfno.yaml

Evaluation

To evaluate a trained model:

python main.py --config configs/adaptfno.yaml --eval

Baseline Models

Configs for CNN and standard FNO are provided under configs/.

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📈 Results

• Task: Short-term climate forecasting (3-day horizon).
• Metric: Temporal Weighted MSE.
• Case Study: Typhoon Yagi trajectory prediction.

AdaptFNO shows improved accuracy in capturing cyclone formation and fine-scale atmospheric dynamics compared to FNO and CNN baselines.

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🔮 Future Work

• Comprehensive benchmarks against CNN and FNO baselines.
• Extension to other extreme events (hurricanes, heat waves, precipitation extremes).
• Integration into operational forecasting pipelines for rapid high-resolution updates.

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📑 Citation

If you use this code, please cite our paper:

@inproceedings{dang2025adaptfno,
  title={AdaptFNO: Adaptive Fourier Neural Operator with Dynamic Spectral Modes and Multiscale Learning for Climate Modeling},
  author={Dang, Hiep Vo and Nguyen, Bach D.G. and Nguyen, Phong C.H. and Hy, Truong-Son},
  booktitle={NeurIPS 2025 Workshop on Machine Learning and the Physical Sciences},
  year={2025}
}

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🤝 Acknowledgements

• ERA5 dataset (ECMWF / Copernicus Climate Data Store).
• Fourier Neural Operator (Li et al., ICLR 2021).
• FourCastNet (Pathak et al., 2022).