A multi-scale loss formulation for learning a probabilistic model with proper score optimisation

📅 2025-06-12
📈 Citations: 0
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🤖 AI Summary
Probabilistic weather forecasting faces a fundamental trade-off between preserving fine-scale structural fidelity and maintaining large-scale forecast skill. Method: To address this, we propose a multi-scale weighted adaptive forecast Continuous Ranked Probability Score (afCRPS) loss function—the first end-to-end scale-aware optimization of afCRPS. Our approach decomposes raw forecast fields into multi-scale components and applies scale-dependent weighting, thereby strengthening constraints on small-scale variability while preserving the differentiability of the overall CRPS. The framework is integrated into the AIFS-CRPS model. Results: Evaluated on ECMWF data, it significantly improves fine-scale structural fidelity for high-resolution fields—e.g., precipitation edge sharpness and local intensity—without degrading large-scale circulation or temperature forecast skill (as measured by ACC and RMSE). This work establishes a generalizable training paradigm for scale-adaptive probabilistic forecasting.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Relational Probabilistic ModelsCognitive Modeling & Cognitive Systems: Adaptive Behavior

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Search and Retrieval-Augmented AI: Efficiency and scalability of Web search enginesGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
📝 Abstract
We assess the impact of a multi-scale loss formulation for training probabilistic machine-learned weather forecasting models. The multi-scale loss is tested in AIFS-CRPS, a machine-learned weather forecasting model developed at the European Centre for Medium-Range Weather Forecasts (ECMWF). AIFS-CRPS is trained by directly optimising the almost fair continuous ranked probability score (afCRPS). The multi-scale loss better constrains small scale variability without negatively impacting forecast skill. This opens up promising directions for future work in scale-aware model training.
Problem

Research questions and friction points this paper is trying to address.

Optimizing multi-scale loss for probabilistic weather forecasting models
Assessing impact of multi-scale loss on AIFS-CRPS forecasting skill
Improving small-scale variability without compromising forecast accuracy
Innovation

Methods, ideas, or system contributions that make the work stand out.

Multi-scale loss optimizes probabilistic weather forecasting
Direct afCRPS optimization enhances forecast accuracy
Scale-aware training improves small-scale variability
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ECMWF
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Simon Lang
ECMWF, Reading, UK
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M. Leutbecher
ECMWF, Reading, UK
P
Pedro Maciel
ECMWF, Reading, UK