Data-Efficient Generative Modeling of Non-Gaussian Global Climate Fields via Scalable Composite Transformations

2026-02-26

AI Summary

This work addresses the challenge of scarce training data in climate modeling—stemming from the high computational cost of climate simulations—which hinders accurate quantification of predictive uncertainty. To overcome this, the authors propose a scalable composite transformation framework that maps non-Gaussian global climate fields to a multivariate standard normal space via nonparametric Bayesian transport maps. The approach jointly models spatial dependence and heavy-tailed marginal distributions by combining parametric marginal models with a semi-parametric B-spline correction. By incorporating a low-rank Gaussian process prior, the method achieves linear computational complexity. Remarkably, using only 10 samples, it accurately reproduces both spatial structure and marginal characteristics across more than 50,000 grid points of global log-precipitation rates, outperforming state-of-the-art methods while using just one-eighth of their training data, thereby substantially improving data efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Quantifying uncertainty in future climate projections is hindered by the prohibitive computational cost of running physical climate models, which severely limits the availability of training data. We propose a data-efficient framework for emulating the internal variability of global climate fields, specifically designed to overcome these sample-size constraints. Inspired by copula modeling, our approach constructs a highly expressive joint distribution via a composite transformation to a multivariate standard normal space. We combine a nonparametric Bayesian transport map for spatial dependence modeling with flexible, spatially varying marginal models, essential for capturing non-Gaussian behavior and heavy-tailed extremes. These marginals are defined by a parametric model followed by a semi-parametric B-spline correction to capture complex distributional features. The marginal parameters are spatially smoothed using Gaussian-process priors with low-rank approximations, rendering the computational cost linear in the spatial dimension. When applied to global log-precipitation-rate fields at more than 50,000 grid locations, our stochastic surrogate achieves high fidelity, accurately quantifying the climate distribution's spatial dependence and marginal characteristics, including the tails. Using only 10 training samples, it outperforms a state-of-the-art competitor trained on 80 samples, effectively octupling the computational budget for climate research. We provide a Python implementation at https://github.com/jobrachem/ppptm .

Problem

• data efficiency
• climate modeling
• non-Gaussian
• uncertainty quantification
• extreme events

Innovation

• data-efficient generative modeling
• composite transformation
• non-Gaussian climate fields
• Bayesian transport map
• spatially varying marginals