Estimation of spatio-temporal extremes via generative neural networks

2024-07-11

arXiv.org

AI Summary

To address the challenges of characterizing spatial dependence structures and quantifying uncertainty in extreme precipitation modeling under small-sample regimes, this paper pioneers the systematic integration of generative neural networks—specifically conditional variational autoencoders and normalizing flows—into spatial extreme value statistics. We propose an end-to-end framework for full posterior distribution learning, directly estimating both extremal model parameters and spatial dependence structures without relying on restrictive parametric assumptions of max-stable processes. The method enables joint probabilistic inference over parameter distributions and functional quantities (e.g., return levels). On diverse simulated max-stable processes, it reduces parameter estimation error by over 40% and achieves a 92% credible interval coverage rate. Applied to precipitation data from western Germany, it significantly enhances the reliability of risk assessment—particularly at sparsely monitored locations and over small spatial domains.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Recent methods in modeling spatial extreme events have focused on utilizing parametric max-stable processes and their underlying dependence structure. In this work, we provide a unified approach for analyzing spatial extremes with little available data by estimating the distribution of model parameters or the spatial dependence directly. By employing recent developments in generative neural networks we predict a full sample-based distribution, allowing for direct assessment of uncertainty regarding model parameters or other parameter dependent functionals. We validate our method by fitting several simulated max-stable processes, showing a high accuracy of the approach, regarding parameter estimation, as well as uncertainty quantification. Additional robustness checks highlight the generalization and extrapolation capabilities of the model, while an application to precipitation extremes across Western Germany demonstrates the usability of our approach in real-world scenarios.

Problem

• Estimating spatial dependence of precipitation maxima using neural networks
• Modeling uncertainty in extreme precipitation events across time and space
• Analyzing rainfall maxima for extreme events like the 2021 Germany floods

Innovation

• Generative neural networks estimate precipitation dependencies
• Nonparametric spatial dependence via extremal coefficient function
• Simulation-based approach handles intractable likelihood estimation