Advanced Torrential Loss Function for Precipitation Forecasting

Accurate precipitation forecasting is becoming increasingly important in the context of climate change. In response, machine learning-based approaches have recently gained attention as an emerging alternative to traditional methods such as numerical weather prediction and climate models. Nonetheless, many recent approaches still rely on off-the-shelf loss functions, and even the more advanced ones merely involve optimization processes based on the critical success index (CSI). The problem, however, is that CSI may become ineffective during extended dry periods when precipitation remains below the threshold, rendering it less than ideal as a criterion for optimization. To address this limitation, we introduce a simple penalty expression and reinterpret it as a quadratic unconstrained binary optimization (QUBO) formulation. Ultimately, the resulting QUBO formulation is relaxed into a differentiable advanced torrential (AT) loss function through an approximation process. The proposed AT loss demonstrates its superiority through the Lipschitz constant, forecast performance evaluations, consistency experiments, and ablation studies with the operational model.