Title: FastNet: Improving the physical consistency of machine-learning weather prediction models through loss function design Show Chinese title

Title: FastNet：通过损失函数设计提高机器学习天气预测模型的物理一致性

Abstract: Machine learning weather prediction (MLWP) models have demonstrated remarkable potential in delivering accurate forecasts at significantly 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 squared error (MSE) loss: (1) a modified spherical harmonic (MSH) loss that penalises spectral amplitude errors to reduce blurring and enhance small-scale structure retention; (2) inclusion of horizontal gradient terms in the loss to suppress non-physical artefacts; 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 \textit{alone} may slightly degrade RMSE scores, when trained in combination the model exhibits very similar MSE performance to an MSE-trained model while at the same time significantly improving 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. Show Chinese abstract

Abstract: 机器学习天气预测（MLWP）模型在与传统数值天气预测（NWP）系统相比，以显著降低的计算成本提供准确预报方面展示了惊人的潜力。 然而，在确保MLWP输出的物理一致性方面仍存在挑战，特别是在确定性设置中。 本研究介绍了FastNet，一个基于图神经网络（GNN）的全球预测模型，并研究了替代损失函数设计对提高其预报物理真实性的效果。 我们探索了标准均方误差（MSE）损失的三个关键修改：（1）一种修改后的球面谐波（MSH）损失，用于惩罚谱振幅误差，以减少模糊并增强小尺度结构保留；（2）在损失中包含水平梯度项，以抑制非物理伪影；（3）一种替代的风表示方法，将速度和方向解耦，以更好地捕捉极端风事件。 结果表明，尽管MSH和基于梯度的损失\textit{单独}可能会略微降低RMSE分数，但当联合训练时，该模型在MSE性能上与MSE训练模型非常相似，同时显著提高了谱保真度和物理一致性。 替代的风表示方法进一步提高了风速准确性并减少了方向偏差。 总体而言，这些发现强调了损失函数设计作为将领域知识嵌入MLWP模型并推进其业务准备度的机制的重要性。