AT Loss: Advanced Torrential Loss Function for Precipitation Forecasting

2025-09-01

AI Summary

Existing precipitation forecasting models suffer from optimization failure under prolonged dry periods (i.e., zero-precipitation events) when trained using the Critical Success Index (CSI), resulting in poor sensitivity to rare, high-impact rainfall events. Method: We propose a differentiable Advanced Thunderstorm Loss function (AT Loss), which reformulates the conventional non-differentiable CSI-based penalty as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Through continuous relaxation and Lipschitz continuity constraints, AT Loss achieves both differentiability and numerical stability. Contribution/Results: AT Loss overcomes CSI’s optimization blind spot during zero-precipitation intervals, substantially improving model discrimination of extreme precipitation. Ablation studies and comparisons with operational forecasting models demonstrate that AT Loss consistently outperforms mainstream loss functions in accuracy, forecast consistency, and robustness—establishing a practical, deployable optimization paradigm for meteorological AI systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Optimizing precipitation forecasting during extended dry periods
• Addressing limitations of critical success index in machine learning
• Developing differentiable loss function for torrential rain prediction

Innovation

• Quadratic unconstrained binary optimization formulation
• Differentiable advanced torrential loss function
• Simple penalty expression addressing dry periods