Colin Minini — CentraleSupélec & University College Dublin
February – July 2025 — HIGHWAVE Project
Supervisors:
Prof. Frédéric Dias — ENS Paris-Saclay & University College Dublin
Prof. Brendan Murphy — University College Dublin
This research project explores hybrid deep learning methods for forecasting ocean wave conditions — in particular, the significant wave height (SWH) recorded by the M6 buoy off the west coast of Ireland.
While physics-based numerical weather prediction (NWP) models provide reliable large-scale forecasts, they often exhibit systematic local biases and limited short-term accuracy.
Here, we design deep neural networks that learn the residuals between numerical forecasts and real observations, effectively correcting physical model outputs through data-driven learning.
This work lies at the intersection of scientific machine learning, time-series forecasting, and physical modeling — bridging AI and oceanography in the context of the EU-funded HIGHWAVE project.
- Reimplement and benchmark state-of-the-art long-term time-series architectures (LSTM, TCN, PatchTST, SegRNN) on benchmark and real datasets.
- Build a robust forecasting pipeline handling missing data and contiguous sliding-window sampling for marine time series.
- Propose a hybrid residual-learning framework combining numerical forecasts (NOAA, ICON, MFWAM, etc.) with deep learning.
- Demonstrate measurable accuracy gains over both standalone deep learning and raw physical forecasts.
├── data # Datasets created, processed and used for the project
├── figures/ # All result plots (below)
├── notebooks # The experimenting notebooks
├── Sea_State_Forecast_Project_Report.pdf # Detailed technical report
├── Sea_State_Forecasting_with_Deep_Learning_and_Hybrid_Residual_Modeling.ipynb # Main research notebook
No installation or setup is required — this repository consists of a single, self-contained Jupyter notebook reproducing all experiments and figures.
| Dataset | Source | Resolution | Purpose |
|---|---|---|---|
| weather.csv | Public meteorological dataset | 10 min | Model benchmarking and architecture testing |
| M6 Observational | Irish Marine Data Buoy Network | 1 h | Real-world univariate SWH forecasting |
| Hybrid (M6 + Forecasts) | NOAA, ICON, MFWAM, StormGlass API merge | 1 h | Hybrid DL + Numerical residual learning |
For each 24-hour horizon (H), models use the past (L = 336) hours to predict the next 24 hours:
In the hybrid setup, models learn residuals:
- LSTM – Recurrent baseline for temporal dependencies
- TCN – Causal dilated convolutions for sequence modeling
- PatchTST – Transformer with patchwise attention for long-context forecasting [Nie et al., 2023]
- SegRNN – Segment Recurrent Neural Network optimized for long-term forecasting [Lin et al., 2024]
- XGBoost – Gradient-boosted tree baseline
Multivariate long-range forecasting reproduces published SOTA results.
SegRNN and PatchTST show the lowest errors and best temporal consistency.
| Model | MAE | MSE | Parameters |
|---|---|---|---|
| LSTM | 0.347 | 0.200 | 68 K |
| TCN | 0.370 | 0.233 | 55 K |
| PatchTST (uni) | 0.266 | 0.133 | 2.6 M |
| PatchTST (multi) | 0.269 | 0.206 | 2.6 M |
| SegRNN (uni) | 0.251 | 0.122 | 1.6 M |
| SegRNN (multi) | 0.227 | 0.187 | 1.6 M |
Physics-based numerical forecasts (e.g., NOAA, ICON, StormGlass) provide essential large-scale information but exhibit systematic local biases at the M6 buoy scale.
To correct these biases, deep learning models were trained to predict residuals between observed and numerically forecasted significant wave height (SWH), effectively combining physical priors with data-driven corrections.
| Rank | Model | MAE | MSE |
|---|---|---|---|
| 1 | NOAA (day 1) | 0.425 | 0.338 |
| 2 | StormGlass AI (day 1) | 0.431 | 0.336 |
| 3 | Meteo SG (day 1) | 0.431 | 0.336 |
| 4 | ICON SG (day 1) | 0.442 | 0.409 |
| 5 | NOAA (day 2) | 0.561 | 0.568 |
The best physical forecasts reach MAE ≈ 0.42 m and MSE ≈ 0.34, forming the baseline for hybrid correction.
| Rank | Model | MAE | MSE | Parameters |
|---|---|---|---|---|
| 1 | LSTM | 0.402 | 0.294 | 56.9 K |
| 2 | SegRNN (uni) | 0.406 | 0.297 | 1.59 M |
| 3 | XGBoost | 0.415 | 0.316 | X |
| 4 | PatchTST (uni) | 0.428 | 0.324 | 406 K |
| 5 | TCN | 0.444 | 0.353 | 43.9 K |
- The hybrid LSTM and SegRNN models achieve MAE ≈ 0.40 m and MSE ≈ 0.29, improving upon the best physical forecast (NOAA day 1, MAE = 0.425, MSE = 0.338) by approximately 5.6 % (MAE) and 13 % (MSE).
- Even lightweight architectures such as LSTM match or surpass the best physics-only baselines, confirming the value of residual correction.
- Tree-based XGBoost remains competitive but less robust across time windows.
- Transformer-based PatchTST yields stable performance with higher computational cost.
Conclusion:
Hybrid residual learning effectively reduces systematic biases in physics-based ocean forecasts, demonstrating that deep learning can serve as a statistical correction layer for numerical wave models.
- LSTM and SegRNN achieved the best overall MAE/MSE trade-off in both standalone and hybrid configurations.
- Residual learning improved physical forecasts by up to 5–6 % in MAE and ≈13 % in MSE relative to the best numerical model.
- Multivariate pretraining enhanced univariate forecasting through shared-weight generalization.
- Extend residual learning to multiple buoys with spatial models (Graph NNs).
- Introduce uncertainty quantification (e.g., Bayesian DL, quantile regression).
- Explore self-supervised pretraining on large-scale meteorological archives.
- Apply the hybrid correction paradigm to climate, energy, and atmospheric forecasting domains.
- Lin S., Lin W., Wu W., Zhao F., Mo R., Zhang H. (2024). Segment Recurrent Neural Network for Long-Term Time Series Forecasting. (https://arxiv.org/abs/2308.11200)
- Nie Y., Nguyen N. H., Sinthong P., Kalagnanam J. (2023). A Time Series is Worth 64 Words: Long-Term Forecasting with Transformers. (https://arxiv.org/abs/2211.14730)
- Kong Y., Wang Z., Nie Y., Zhou T., Zohren S., Liang Y., Sun P., Wen Q. (2023). Unlocking the Power of LSTM for Long-Term Time Series Forecasting. (https://arxiv.org/abs/2408.10006)
- Wen Q., Zhou T., Zhang C., Chen W., Ma Z., Yan J., Sun L. (2023). Transformers in Time Series: A Survey. (https://arxiv.org/abs/2202.07125)
- Bai S., Kolter J. Z., Koltun V. (2018). An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling. (https://arxiv.org/abs/1803.01271)
For questions or collaborations: colin.minini@student-cs.fr