标题： 不要将均方根误差作为降水目标！ 显示英文标题

标题： Stop using root-mean-square error as a precipitation target!

摘要： 均方根误差（RMSE）仍然是数据驱动的降水模型的默认训练损失，尽管降水是半连续的、零膨胀的、严格非负的且尾部厚重的。 这种高斯假设的目标函数错误地指定了数据生成过程，因为它容忍负预测，对罕见的极端事件惩罚不足，并忽略了零点的质量。 我们建议用Tweedie偏差代替RMSE，这是一种基于似然且可微的损失函数，属于指数-离散族，其方差函数为$V(\mu)=\mu^p$。 对于$1<p<2$，它产生一个在零点有质量点且$y>0$有连续密度的复合泊松-伽马分布，与观测到的降水特征相匹配。 我们（i）从方差-均值幂律估计$p$，并表明不同时间聚合下的降水远非高斯分布，Tweedie幂$p$随着累积长度的增加而向伽马极限增长；以及（ii）证明在使用Tweedie偏差代替RMSE训练深度数据驱动模型时，技能表现一致提高。 在北京的扩散模型降尺度中，Tweedie损失提高了湿像素的平均绝对误差和极端召回率（$\sim0.60$与$0.50$在第99百分位）。 在加尔各答的ConvLSTM现在预测中，Tweedie损失提高了湿像元的MAE和干像元命中率，这些改进随着领先时间的增加而逐步累积（对于MAE，$\sim2%$在$t{+}1$增长到$\sim16%$在$t{+}4$）。 由于Tweedie偏差在$p$上是连续的，它在不同尺度上平滑适应，为基于降水的学习任务提供了统计上有依据的实际替代RMSE的方法。 显示英文摘要

摘要： Root-mean-square error (RMSE) remains the default training loss for data-driven precipitation models, despite precipitation being semi-continuous, zero-inflated, strictly non-negative, and heavy-tailed. This Gaussian-implied objective misspecifies the data-generating process because it tolerates negative predictions, underpenalises rare heavy events, and ignores the mass at zero. We propose replacing RMSE with the Tweedie deviance, a likelihood-based and differentiable loss from the exponential--dispersion family with variance function $V(\mu)=\mu^p$. For $1<p<2$ it yields a compound Poisson--Gamma distribution with a point mass at zero and a continuous density for $y>0$, matching observed precipitation characteristics. We (i) estimate $p$ from the variance--mean power law and show that precipitation across temporal aggregations is far from Gaussian, with the Tweedie power $p$ increasing with accumulation length towards a Gamma limit; and (ii) demonstrate consistent skill gains when training deep data-driven models with Tweedie deviance in place of RMSE. In diffusion-model downscaling over Beijing, Tweedie loss improves wet-pixel MAE and extreme recall ($\sim0.60$ vs $0.50$ at the 99th percentile). In ConvLSTM nowcasting over Kolkata, Tweedie loss yields improved wet-pixel MAE and dry-pixel hit rates, with improvements that compound autoregressively with lead time (for MAE, $\sim2%$ at $t{+}1$ growing to $\sim16%$ at $t{+}4$). Because the Tweedie deviance is continuous in $p$, it adapts smoothly across scales, offering a statistically justified, practical replacement for RMSE in precipitation-based learning tasks.