傅里叶幅度与相关损失：超越L2损失的精准降水临近预报
Fourier Amplitude and Correlation Loss: Beyond Using L2 Loss for Skillful Precipitation Nowcasting
AI总结：
针对降水临近预报中深度学习预测模糊的问题，提出由傅里叶幅度损失和相关损失组成的FACL损失替代传统L2损失，同时引入区域直方图散度优化气象评分，在多数据集上验证了方法的有效性。
摘要：
近年来，深度学习方法已被广泛应用于降水临近预报领域。以往研究主要聚焦于提出新的模型架构以提升逐像素指标，但这类方法往往会生成模糊的预测结果，对预报业务的实用价值有限。本研究提出了一种全新的傅里叶幅度与相关损失（FACL），它由两个新颖的损失项组成：傅里叶幅度损失（FAL）和傅里叶相关损失（FCL）。其中FAL对模型预测的傅里叶幅度进行正则化，FCL则补充缺失的相位信息。这两个损失项协同作用，可替代传统的$L_2$损失（如均方误差MSE和加权MSE），用于解决基于信号的数据的时空预测问题。该方法具有通用性、无参数且高效的特点。我们在1个合成数据集和3个雷达回波数据集上开展了大量实验，结果表明，该方法在仅小幅牺牲逐像素精度和结构相似性的前提下，提升了感知指标和气象技能评分。此外，为了缩小临界成功指数（CSI）、分数技能评分（FSS）等气象技能评分的误差余量，我们提出并采用了区域直方图散度（RHD）——这是一种考虑基于信号的图像模式间块级相似性、且对局部变换具有容忍度的距离度量。代码已开源至https://github.com/argenycw/FACL。
英文摘要：
Deep learning approaches have been widely adopted for precipitation nowcasting in recent years. Previous studies mainly focus on proposing new model architectures to improve pixel-wise metrics. However, they frequently result in blurry predictions which provide limited utility to forecasting operations. In this work, we propose a new Fourier Amplitude and Correlation Loss (FACL) which consists of two novel loss terms: Fourier Amplitude Loss (FAL) and Fourier Correlation Loss (FCL). FAL regularizes the Fourier amplitude of the model prediction and FCL complements the missing phase information. The two loss terms work together to replace the traditional $L_2$ losses such as MSE and weighted MSE for the spatiotemporal prediction problem on signal-based data. Our method is generic, parameter-free and efficient. Extensive experiments using one synthetic dataset and three radar echo datasets demonstrate that our method improves perceptual metrics and meteorology skill scores, with a small trade-off to pixel-wise accuracy and structural similarity. Moreover, to improve the error margin in meteorological skill scores such as Critical Success Index (CSI) and Fractions Skill Score (FSS), we propose and adopt the Regional Histogram Divergence (RHD), a distance metric that considers the patch-wise similarity between signal-based imagery patterns with tolerance to local transforms. Code is available at https://github.com/argenycw/FACL
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