Multi-source constrained Machine Learning for oceanic parameters forecasting

This study evaluates multi-source fusion techniques for environmental forecasting, focusing on their effectiveness in predicting oceanic and atmospheric variables. Three neural network architectures are examined: a baseline LSTM model, a Softmax Fusion model, and a Lagrangian Fusion model. A central component of the approach is the incorporation of physicsbased constraints during training to ensure physically consistent predictions. Results based on Root Mean Squared Error (RMSE) indicate that fusion-based models consistently outperform the baseline for wave-related and thermodynamic variables such as air and water temperature. RMSE reductions for these variables range from approximately 5% to over 40%, driven by the models' ability to enforce spatiotemporal smoothness and reduce spatial variability. In contrast, wind components show higher RMSE in fusion models, highlighting a trade-off between global physical consistency and the accurate representation of localized, highvariance wind phenomena. These findings demonstrate the advantages of fusion architectures for improving buoy-based wave and thermodynamic forecasts, while suggesting that future work on wind predictions may benefit from adaptive regularization or hybrid loss functions to capture both global coherence and local detail better.