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

2026-05-04

AI Summary

This work addresses the challenge of modeling complex spatiotemporal fields characterized by nonstationarity, non-Gaussianity, and highly nonlinear dependencies. The authors propose a generative approach based on autoregressive transport maps, which decomposes the joint density into univariate conditional distributions. Each conditional distribution is modeled using a Gaussian process, and a data-driven sparse conditioning set is introduced to ensure scalability in high dimensions. By incorporating Gaussian process priors as regularizers, the method enhances generalization under limited data and enables forward prediction and sampling from incomplete trajectories. The approach demonstrates both high accuracy and computational efficiency when validated on non-Gaussian climate model outputs comprising tens of millions of spatial points.

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.

Problem

• spatio-temporal fields
• non-Gaussian
• generative modeling
• nonstationary
• scalability

Innovation

• autoregressive transport maps
• Gaussian processes
• non-Gaussian spatio-temporal fields
• scalable generative modeling
• data-dependent sparsity