Generative multi-fidelity modeling and downscaling via spatial autoregressive transport maps

2025-09-26

AI Summary

High-fidelity spatial field data are costly to acquire and scarce, whereas low-fidelity data are abundant but insufficiently accurate. Method: This paper proposes a scalable Bayesian multi-fidelity modeling framework centered on a fidelity-aware autoregressive Gaussian process. It couples a spatial autoregressive transport map with a conjugate regularized prior, enabling closed-form probabilistic inference and efficient hyperparameter optimization under small-sample regimes. The framework supports analytical expressions for high-fidelity conditional field distributions and rapid computation of integrated likelihoods. Contribution/Results: It accommodates non-Gaussian and non-stationary fields, accurately capturing nonlinear cross-fidelity dependencies and joint distributional structure. In climate field downscaling, it significantly outperforms existing methods: using only coarse-resolution circulation model outputs, it generates statistically faithful representations and reproducible stochastic simulations of fine-scale climate variables.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Spatial fields are often available at multiple fidelities or resolutions, where high-fidelity data is typically more costly to obtain than low-fidelity data. Statistical surrogates or emulators can predict high-fidelity fields from cheap low-fidelity output. We propose a highly scalable Bayesian approach that can learn the joint non-Gaussian distribution and nonlinear dependence structure of nonstationary spatial fields at multiple fidelities from a small number of training samples. Our method is based on fidelity-aware autoregressive GPs with suitably chosen regularization-inducing priors. Exploiting conjugacy, the integrated likelihood is available in closed form, enabling efficient hyperparameter optimization via stochastic gradient descent. After training, the method also characterizes in closed form the distribution of higher-fidelity fields given lower-fidelity data. In our numerical comparisons, we show that our approach substantially outperforms existing methods and that it can be used to characterize and simulate high-fidelity fine-scale climate behavior based on output from coarse (low-fidelity) global circulation models.

Problem

• Predicting high-fidelity spatial fields from low-fidelity data
• Learning joint non-Gaussian distributions of multi-fidelity spatial fields
• Characterizing fine-scale climate behavior using coarse model outputs

Innovation

• Bayesian spatial autoregressive transport maps
• Fidelity-aware Gaussian processes with priors
• Closed-form likelihood for efficient optimization