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arXiv · 2605.03152

Scalable generative modeling of non-Gaussian spatio-temporal fields via autoregressive Gaussian processes

Carrie J. Lei-Cramer·Jian Cao·Matthias Katzfuss
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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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Carrie J. Lei-Cramer, Jian Cao, Matthias Katzfuss. 2026-05-04. Scalable generative modeling of non-Gaussian spatio-temporal fields via autoregressive Gaussian processes. https://arxiv.org/abs/2605.03152

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