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

TL;DR

This paper introduces a scalable autoregressive Gaussian process method for modeling complex, non-Gaussian spatio-temporal fields, suitable for climate data with high dimensionality and limited training samples.

Contribution

It presents a novel autoregressive transport-map approach that models non-Gaussian dependencies and ensures scalability and regularization for high-dimensional spatio-temporal data.

Findings

Accurately models non-Gaussian climate-model output with tens of millions of data points.

Provides a scalable, data-efficient method suitable for small training datasets.

Demonstrates effectiveness in predicting and sampling from incomplete spatio-temporal trajectories.

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.