Extreme-value forest fire prediction A study of the Loss Function in an Ordinality Scheme

TL;DR

This paper tackles predicting extreme wildfire events by reframing wildfire severity as an ordinal multi-class task aligned with operational decisions in France. It systematically compares loss-function designs—such as WKLoss, GWDL, MCEWK, BCE All-Threshold, and a probabilistic TDeGPD approach—across diverse neural architectures, including GraphCast variants, using a large department-level dataset. The findings show that ordinal losses, particularly WKLoss, yield meaningful gains on extreme classes (up to ~0.1 IoU) and improve model robustness, though predicting the rarest events remains challenging due to data imbalance. The work highlights the value of incorporating severity ordering and calibration-aware evaluation, and points to seasonality and uncertainty as key directions for making extreme-event forecasts more reliable in practice.

Abstract

Wildfires are highly imbalanced natural hazards in both space and severity, making the prediction of extreme events particularly challenging. In this work, we introduce the first ordinal classification framework for forecasting wildfire severity levels directly aligned with operational decision-making in France. Our study investigates the influence of loss-function design on the ability of neural models to predict rare yet critical high-severity fire occurrences. We compare standard cross-entropy with several ordinal-aware objectives, including the proposed probabilistic TDeGPD loss derived from a truncated discrete exponentiated Generalized Pareto Distribution. Through extensive benchmarking over multiple architectures and real operational data, we show that ordinal supervision substantially improves model performance over conventional approaches. In particular, the Weighted Kappa Loss (WKLoss) achieves the best overall results, with more than +0.1 IoU (Intersection Over Union) gain on the most extreme severity classes while maintaining competitive calibration quality. However, performance remains limited for the rarest events due to their extremely low representation in the dataset. These findings highlight the importance of integrating both severity ordering, data imbalance considerations, and seasonality risk into wildfire forecasting systems. Future work will focus on incorporating seasonal dynamics and uncertainty information into training to further improve the reliability of extreme-event prediction.

Figures (13)

• Figure 1: Diagram of the proposed study pipeline, including data preprocessing, model training with TDeGPD and WKLOSS, and prediction.
• Figure 2: An ordinal schema is built in the database. Each class represents a number of fires in each department $y$, with classes ordered as $y_0 < y_1 < y_2 < y_3 < y_4$, where $y_0$ represents no fire and $y_4$ represents an extreme number of fires and burned area.
• Figure 3: Distribution of FO (a) and BA-rooted (b) classes risk in the Mediterranean basin and the rest of France. Histograms have been computed relative to the category -Mediterranean (orange) or not (blue).
• Figure 4: Comparison between the raw fire signal and the classification produced by K-Means in the Bouches-du-Rhône for the year 2023.
• Figure 5: Models family type used in this study.

Theorems & Definitions (1)

• Definition 1