Scalable generative modeling of non-Gaussian spatio-temporal fields via autoregressive Gaussian processes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917460626636800 |
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| author | Lei-Cramer, Carrie J. Cao, Jian Katzfuss, Matthias |
| author_facet | Lei-Cramer, Carrie J. Cao, Jian Katzfuss, Matthias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03152 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scalable generative modeling of non-Gaussian spatio-temporal fields via autoregressive Gaussian processes Lei-Cramer, Carrie J. Cao, Jian Katzfuss, Matthias Methodology 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. |
| title | Scalable generative modeling of non-Gaussian spatio-temporal fields via autoregressive Gaussian processes |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.03152 |