# Modeling Spatio-temporal Extremes via Conditional Variational Autoencoders

arXiv: https://arxiv.org/abs/2512.06348 · HTML: https://mlsanity.com/paper/2512.06348/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Advances in Statistical Modeling of Spatial Extremes](https://mlsanity.com/paper/2007.00774/) (2020)
- [Modeling spatial processes with unknown extremal dependence class](https://mlsanity.com/paper/1703.06031/) (2017)
- [Modeling Extremal Streamflow using Deep Learning Approximations and a Flexible Spatial Process](https://mlsanity.com/paper/2208.03344/) (2022)
- [Modeling asymptotically independent spatial extremes based on Laplace random fields](https://mlsanity.com/paper/1507.02537/) (2015)
- [Higher-dimensional spatial extremes via single-site conditioning](https://mlsanity.com/paper/1912.06560/) (2019)
- [Explaining the unexplainable: leveraging extremal dependence to characterize the 2021 Pacific Northwest heatwave](https://mlsanity.com/paper/2307.03688/) (2023)
- [Extreme quantile regression with deep learning](https://mlsanity.com/paper/2404.09154/) (2024)
- [Efficient inference and simulation for elliptical Pareto processes](https://mlsanity.com/paper/1401.0168/) (2013)
- [Bridging Asymptotic Independence and Dependence in Spatial Extremes Using Gaussian Scale Mixtures](https://mlsanity.com/paper/1610.04536/) (2016)
- [An Efficient Workflow for Modelling High-Dimensional Spatial Extremes](https://mlsanity.com/paper/2210.00760/) (2022)
- [Flexible space-time models for extreme data](https://mlsanity.com/paper/2411.19184/) (2024)
- [Spatial scale-aware tail dependence modeling for high-dimensional spatial extremes](https://mlsanity.com/paper/2412.07957/) (2024)
- [Max-infinitely divisible models and inference for spatial extremes](https://mlsanity.com/paper/1801.02946/) (2018)
- [Reconstructing Spatiotemporal Data with C-VAEs](https://mlsanity.com/paper/2307.06243/) (2023)
- [Modeling high and low extremes with a novel dynamic spatio-temporal model](https://mlsanity.com/paper/2508.01481/) (2025)

## Abstract (arXiv)

Extreme weather events are widely studied in fields such as agriculture, ecology, and meteorology. The spatio-temporal co-occurrence of extreme events can strengthen or weaken under changing climate conditions. In this paper, we propose a novel approach to model spatio-temporal extremes by integrating climate indices via a conditional variational autoencoder (cXVAE). A convolutional neural network (CNN) is embedded in the decoder to convolve climatological indices with the spatial dependence within the latent space, thereby allowing the decoder to be dependent on the climate variables. There are three main contributions here. First, we demonstrate through extensive simulations that the proposed conditional XVAE accurately emulates spatial fields and recovers spatially and temporally varying extremal dependence with very low computational cost post training. Second, we provide a simple, scalable approach to detecting condition-driven shifts and whether the dependence structure is invariant to the conditioning variable. Third, when dependence is found to be condition-sensitive, the conditional XVAE supports counterfactual experiments allowing intervention on the climate covariate and propagating the associated change through the learned decoder to quantify differences in joint tail risk, co-occurrence ranges, and return metrics. To demonstrate the practical utility and performance of the model in real-world scenarios, we apply our method to analyze the monthly maximum Fire Weather Index (FWI) over eastern Australia from 2014 to 2024 conditioned on the El Ni~no/Southern Oscillation (ENSO) index.