Fourier Amplitude and Correlation Loss: Beyond Using L2 Loss for Skillful Precipitation Nowcasting

TL;DR

A new Fourier Amplitude and Correlation Loss (FACL) which consists of two novel loss terms: Fourier Amplitude Loss (FAL) and Fourier Correlation Loss (FCL), which regularizes the Fourier amplitude of the model prediction and complements the missing phase information.

Abstract

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

Figures (14)

• Figure 1: The pre-defined probability threshold function $P(t)$ over training steps $t$ with $T$ total steps. $\alpha$ determines the ratio of the training steps where $P(t)=0$.
• Figure 2: Output frames of the ConvLSTM model trained with different losses on Stochastic Moving-MNIST. From top to bottom: Input, Ground Truth, MSE, FACL.
• Figure 3: Output frames of the Earthformer models trained with MSE and FACL on SEVIR.
• Figure 4: FAL loss terms over different values of (left) $\sigma$ in blurring and (right) $t$ in translation. In (right), $L_2$ (the blue line) and $|\sum{2X\hat{X}} - \sum{2|F||\hat{F}|}|$ (the green line) mostly overlap.
• Figure 5: Qualitative performance of different losses for ConvLSTM on Stochastic Moving-MNIST.