# Modelling and simulating spatial extremes by combining extreme value theory with generative adversarial networks

arXiv: https://arxiv.org/abs/2111.00267 · HTML: https://mlsanity.com/paper/2111.00267/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 76 references that are in the map.
- First posted on arXiv 30 Oct 2021.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [StackGAN: Text to Photo-realistic Image Synthesis with Stacked Generative Adversarial Networks](https://mlsanity.com/paper/1612.03242/) (2016)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [A Variational Inequality Perspective on Generative Adversarial Networks](https://mlsanity.com/paper/1802.10551/) (2018)
- [One-Class Adversarial Nets for Fraud Detection](https://mlsanity.com/paper/1803.01798/) (2018)
- [ExGAN: Adversarial Generation of Extreme Samples](https://mlsanity.com/paper/2009.08454/) (2020)
- [Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions](https://mlsanity.com/paper/2101.09113/) (2021)
- [Copula & Marginal Flows: Disentangling the Marginal from its Joint](https://mlsanity.com/paper/1907.03361/) (2019)
- [Gradient boosting for extreme quantile regression](https://mlsanity.com/paper/2103.00808/) (2021)
- [Sparse Structures for Multivariate Extremes](https://mlsanity.com/paper/2004.12182/) (2020)
- [Using generative adversarial networks to synthesize artificial financial datasets](https://mlsanity.com/paper/2002.02271/) (2020)
- [Extremes on river networks](https://mlsanity.com/paper/1501.02663/) (2015)
- [Non-Stationary Dependence Structures for Spatial Extremes](https://mlsanity.com/paper/1411.3174/) (2014)
- [Bayesian inference for multivariate extreme value distributions](https://mlsanity.com/paper/1611.05602/) (2016)
- [Modeling Feature Representations for Affective Speech using Generative Adversarial Networks](https://mlsanity.com/paper/1911.00030/) (2019)
- [Extremal Behavior of Aggregated Data with an Application to Downscaling](https://mlsanity.com/paper/1712.09816/) (2017)

## Abstract (arXiv)

Modelling dependencies between climate extremes is important for climate risk assessment, for instance when allocating emergency management funds. In statistics, multivariate extreme value theory is often used to model spatial extremes. However, most commonly used approaches require strong assumptions and are either too simplistic or over-parameterized. From a machine learning perspective, Generative Adversarial Networks (GANs) are a powerful tool to model dependencies in high-dimensional spaces. Yet in the standard setting, GANs do not well represent dependencies in the extremes. Here we combine GANs with extreme value theory (evtGAN) to model spatial dependencies in summer maxima of temperature and winter maxima in precipitation over a large part of western Europe. We use data from a stationary 2000-year climate model simulation to validate the approach and explore its sensitivity to small sample sizes. Our results show that evtGAN outperforms classical GANs and standard statistical approaches to model spatial extremes. Already with about 50 years of data, which corresponds to commonly available climate records, we obtain reasonably good performance. In general, dependencies between temperature extremes are better captured than dependencies between precipitation extremes due to the high spatial coherence in temperature fields. Our approach can be applied to other climate variables and can be used to emulate climate models when running very long simulations to determine dependencies in the extremes is deemed infeasible.