通过改进损失函数,让机器学习天气模型更符合物理规律。
FastNet: Improving the physical consistency of machine-learning weather prediction models through loss function design
- 用谱域误差和梯度项惩罚,减少预测中的虚假结构。
- 组合使用多种损失后,准确率接近传统方法,但物理一致性显著提升。
- 特别适合需要高物理真实性的气象预测场景。
机器学习天气预测(MLWP)模型在计算成本远低于传统数值天气预报(NWP)系统的同时,展现出高精度潜力。然而,在确定性设置下,其输出的物理一致性仍面临挑战。本研究提出基于图神经网络(GNN)的全球预测模型FastNet,探索不同损失函数设计对提升预测物理真实性的效果。重点改进标准均方误差(MSE)损失:(1)引入改进球谐函数(MSH)损失,惩罚谱幅误差以减少模糊并保留小尺度结构;(2)在损失中加入水平梯度项,抑制非物理解析伪影;(3)采用解耦风速与风向的表示方式,更好捕捉极端风事件。结果表明,尽管单独使用MSH或梯度损失可能轻微降低RMSE,但联合训练时,模型在保持与MSE模型相当的均方误差表现的同时,显著提升谱保真度与物理一致性。解耦风表示进一步提高了风速预测精度并减小方向偏差。研究强调,损失函数设计是嵌入领域知识、提升MLWP模型实用性的关键机制。
原文摘要 · Abstract (English)
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.
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