FastNet: Improving the Physical Consistency of Machine Learning Weather Prediction Models through Loss Function Design

Abstract Machine learning weather prediction (MLWP) models have demonstrated remarkable potential in delivering accurate forecasts at substantially reduced computational cost compared to traditional numerical weather prediction (NWP) systems. However, challenges remain in ensuring the physical consistency of MLWP outputs, particularly in deterministic settings. This study presents FastNet, a graph neural network (GNN)-based global prediction model, and investigates the impact of alternative loss function designs on improving the physical realism of its forecasts. We explore three key modifications to the standard mean-square error (MSE) loss: 1) a modified spherical harmonic (MSH) loss that penalizes spectral amplitude errors to reduce blurring and enhance small-scale structure retention, 2) inclusion of horizontal gradient terms in the loss to suppress nonphysical artifacts, and 3) an alternative wind representation that decouples speed and direction to better capture extreme wind events. Results show that while the MSH and gradient-based losses alone may slightly degrade root MSE (RMSE) scores, when trained in combination, the model exhibits very similar MSE performance to an MSE-trained model while at the same time much improved spectral fidelity and physical consistency. The alternative wind representation further improves wind speed accuracy and reduces directional bias. Collectively, these findings highlight the importance of loss function design as a mechanism for embedding domain knowledge into MLWP models and advancing their operational readiness.