Park et al. (2025) Unicorn: U-Net for sea ice forecasting with convolutional neural ordinary differential equations

Identification

• Journal: Scientific Reports
• Year: 2025
• Date: 2025-10-17
• Authors: Jaesung Park, Yoonseo Cho, Jong-June Jeon, Jinku Park, Hyun‐Cheol Kim, Sungchul Hong
• DOI: 10.1038/s41598-025-20097-4

Research Groups

• Financial Consulting Business Department, Korea Rating & Data, Seoul, Republic of Korea
• Department of Statistical Data Science, University of Seoul, Seoul, Republic of Korea
• Center of Remote Sensing and GIS, Korea Polar Research Institute, Incheon, Republic of Korea
• Department of Statistics, Changwon National University, Changwon, Republic of Korea

Short Summary

This paper introduces Unicorn, a novel deep learning architecture integrating U-Net with convolutional neural ordinary differential equations (ConvNODE) and time series decomposition, to forecast weekly sea ice concentration and extent in the Arctic. Through real data analysis from 1998 to 2021, Unicorn significantly outperforms state-of-the-art models, achieving a 12% average MAE improvement for sea ice concentration and an 18% improvement in IIEE for sea ice extent forecasting.

Objective

• To develop an efficient deep learning model for accurate weekly sea ice concentration (SIC) and sea ice extent (SIE) forecasting in the Arctic.
• To overcome limitations of existing sea ice forecasting models by integrating multiple time series images, capturing spatiotemporal dynamics using convolutional neural ordinary differential equations (ConvNODE) in a U-Net bottleneck, and addressing non-stationarity through time series decomposition.

Study Configuration

• Spatial Scale: Pan-Arctic region. Sea ice images are mapped to a 25 km x 25 km grid, with a uniform resolution of 448 x 304 pixels. Metrics are computed using pixel values within non-land ice areas.
• Temporal Scale: Weekly sea ice forecasting. The study utilizes observational data from June 22, 1998, to June 14, 2021 (23 years). The model forecasts 4 weeks ahead ((\tau=4)) using information from the preceding 12 weeks ((L=12)). A time series cross-validation strategy divides data into four overlapping 15-year periods (11 years for training, 1 year for validation, 3 years for testing).

Methodology and Data

• Models used:
  • Unicorn (U-Net for sea Ice forecasting using Convolutional OpeRation Node): The proposed model, featuring a U-Net architecture, convolutional neural ordinary differential equations (ConvNODE) in the bottleneck layer for spatiotemporal latent modeling, and a decomposition (DCMP) method to separate input images into trend and residual components. It also integrates ancillary data.
  • Benchmark models: CNN, ConvLSTM, U-Net, DU-Net (Decomposition U-Net), NU-Net, SICNet (CBAM), SICNet (TSAM).
• Data sources:
  • Sea Ice Concentration (SIC): Observational weekly average data from the National Snow and Ice Data Center (NSIDC), derived from Defense Meteorological Satellite Program (DMSP) sensors, 25 km x 25 km grid.
  • Brightness Temperature (TB): NSIDC, from DMSP Special Sensor Microwave/Imager (SSMI) and Special Sensor Microwave Image/Sounder (SSMIS) sensors, 37 GHz frequency channel, preprocessed to weekly average and 25 km x 25 km grid.
  • Sea-Ice Age (SIA): NSIDC, categorized into first-year ice (FYI) and multi-year ice (MYI), preprocessed to weekly and 25 km x 25 km grid.

Main Results

• Sea Ice Concentration (SIC) Forecasting:
  • Unicorn significantly outperforms all benchmark models in Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE).
  • Achieved an average MAE improvement of 12.11% compared to benchmark models, and 4.17% compared to the next best model (SICNet (CBAM)).
  • Achieved an average RMSE improvement of 11.60% compared to benchmark models, and 4.05% compared to SICNet (CBAM).
  • Demonstrated the lowest average errors at each target time point (1 to 4 weeks ahead).
  • Showed superior performance during periods of decreasing sea ice (e.g., June to October).
• Sea Ice Extent (SIE) Forecasting:
  • Unicorn outperforms state-of-the-art models across Integrated Ice-Edge Error (IIEE), mean Intersection over Union (mIoU), and F1-score metrics.
  • Exhibited an average IIEE improvement of 17.59% compared to benchmark models, and 7.55% compared to SICNet (CBAM).
  • Maintained the lowest IIEE at each target time point.
  • Demonstrated superior performance in highly dynamic First-Year Ice (FYI) regions, which are critical for evaluating dynamic performance.
• Ablation Study:
  • The removal of ancillary data (Brightness Temperature and Sea-Ice Age) had the most substantial impact on performance, causing significant declines (e.g., MAE increased by 4.20%, IIEE by 7.73%).
  • The omission of ConvNODE resulted in notable accuracy losses (e.g., MAE increased by 1.30%, RMSE by 2.62%), highlighting its essential role.
  • The Decomposition (DCMP) block proved effective in scenarios with distribution shifts (e.g., decreasing and increasing SIC patterns).

Contributions

• Proposed an efficient deep learning architecture (Unicorn) for fusing sea ice concentration (SIC) image time series and ancillary static images (brightness temperature, sea-ice age) to enhance forecasting accuracy.
• Introduced a novel spatiotemporal latent modeling approach utilizing neural ordinary differential equations with convolutional operations (ConvNODE) within the U-Net bottleneck to capture complex dynamics.
• Demonstrated superior performance over state-of-the-art models in both SIC and SIE forecasting for 1 to 4 weeks ahead through real data analysis from 1998 to 2021.

Funding

• Global - Learning & Academic research institution for Master’s·PhD students, and Postdocs(LAMP) Program of the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. RS-2024-00444460).
• National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2022-NR068754) (Jaesung Park).
• 2024 sabbatical year research grant of the University of Seoul (Jong-June Jeon).

Citation

@article{Park2025Unicorn,
  author = {Park, Jaesung and Cho, Yoonseo and Jeon, Jong-June and Park, Jinku and Kim, Hyun‐Cheol and Hong, Sungchul},
  title = {Unicorn: U-Net for sea ice forecasting with convolutional neural ordinary differential equations},
  journal = {Scientific Reports},
  year = {2025},
  doi = {10.1038/s41598-025-20097-4},
  url = {https://doi.org/10.1038/s41598-025-20097-4}
}