Scalable generative modeling of non-Gaussian spatio-temporal fields via autoregressive Gaussian processes
Abstract
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across space and time and are nonlinear, resulting in nonstationary and non-Gaussian joint distributions. Our approach represents the joint density of a spatio-temporal field as a product of univariate conditional distributions and models these conditionals using Gaussian processes within an autoregressive transport-map construction. This prior distribution provides regularization, making our method suitable for a small number of training samples. Data-dependent sparsity in the conditioning sets ensures scalability to high-dimensional distributions. We also propose a variant of the method designed to sample or predict forward in time from a given incomplete space-time trajectory. We demonstrate the accuracy and scalability of our approach on non-Gaussian climate-model output with tens of millions of data points.
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BibTeX
@misc{leicramer2026scalable,
title = {{Scalable generative modeling of non-Gaussian spatio-temporal fields via autoregressive Gaussian processes}},
author = {Carrie J. Lei-Cramer and Jian Cao and Matthias Katzfuss},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.03152},
eprint = {2605.03152},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.03152},
}
RIS
TY - UNPB
TI - Scalable generative modeling of non-Gaussian spatio-temporal fields via autoregressive Gaussian processes
AU - Carrie J. Lei-Cramer
AU - Jian Cao
AU - Matthias Katzfuss
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2605.03152
UR - https://arxiv.org/abs/2605.03152
AB - Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across space and time and are nonlinear, resulting in nonstationary and non-Gaussian joint distributions. Our approach represents the joint density of a spatio-temporal field as a product of univariate conditional distributions and models these conditionals using Gaussian processes within an autoregressive transport-map construction. This prior distribution provides regularization, making our method suitable for a small number of training samples. Data-dependent sparsity in the conditioning sets ensures scalability to high-dimensional distributions. We also propose a variant of the method designed to sample or predict forward in time from a given incomplete space-time trajectory. We demonstrate the accuracy and scalability of our approach on non-Gaussian climate-model output with tens of millions of data points.
ER -