Modeling Spatial Extremal Dependence of Precipitation Using Distributional Neural Networks

arXiv stat.ML / 5/1/2026

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Key Points

The paper introduces a simulation-based estimation method that uses generative neural networks to model spatiotemporal dependence of precipitation maxima and quantify uncertainty.
Framed within max-stable processes for extremes, the approach estimates model parameters with uncertainty and produces an explicit nonparametric estimate of spatial dependence via the pairwise extremal coefficient function.
The authors validate the method through extensive finite-sample studies, showing strong performance in complex scenarios where closed-form likelihood estimation is not feasible.
They apply the technique to monthly rainfall maxima in Western Germany (2021–2023), a period that includes a deadly extreme precipitation and consecutive flooding event in July 2021.
The paper argues that the core generative ideas could generalize to other applications beyond precipitation modeling.

Abstract

In this work, we propose a simulation-based estimation approach using generative neural networks to determine dependencies of precipitation maxima and their underlying uncertainty in time and space. Within the common framework of max-stable processes for extremes under temporal and spatial dependence, our methodology allows estimating the process parameters and their respective uncertainty, but also delivers an explicit nonparametric estimate of the spatial dependence through the pairwise extremal coefficient function. We illustrate the effectiveness and robustness of our approach in a thorough finite sample study where we obtain good performance in complex settings for which closed-form likelihood estimation becomes intractable. We use the technique for studying monthly rainfall maxima in Western Germany for the period 2021-2023, which is of particular interest since it contains an extreme precipitation and consecutive flooding event in July 2021 that had a massive deadly impact. Beyond the considered setting, the presented methodology and its main generative ideas also have great potential for other applications.