A new framework for non-stationary spatio-temporal data fusion of multi-fidelity models

Fuente: arXiv
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Main Authors: Colombo, Pietro, Sigrist, Fabio, Miller, Claire, O'Donnell, Ruth, Yang, Xiaochen, Maranzano, Paolo
Format: Preprint
Published: 2026
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author Colombo, Pietro
Sigrist, Fabio
Miller, Claire
O'Donnell, Ruth
Yang, Xiaochen
Maranzano, Paolo
author_facet Colombo, Pietro
Sigrist, Fabio
Miller, Claire
O'Donnell, Ruth
Yang, Xiaochen
Maranzano, Paolo
contents We propose a new scalable framework for spatio-temporal data fusion with multi-fidelity Gaussian processes (MFGPs) that enables fully likelihood-based inference for both stationary and non-stationary fidelity integration. The framework is designed for environmental applications, where abundant but noisy low-fidelity data (e.g., satellite or reanalysis products) must be fused with sparse yet accurate high-fidelity in-situ observations to obtain high-resolution reconstructions. Our key methodological contribution is a decomposed multi-fidelity covariance formulation that allows the Vecchia approximation to be applied directly to the latent low-fidelity and discrepancy processes. Combined with a Woodbury-based reconstruction, this yields a numerically stable and computationally efficient evaluation of the joint marginal likelihood without ever forming the full multi-fidelity covariance matrix. In addition, we introduce a generalized least squares (GLS) mean-removal strategy with fidelity-specific offsets, preventing systematic biases from being absorbed into cross-fidelity dependence. We validate the proposed approach through extensive experiments on synthetic data and a large-scale real-world application to wind speed reconstruction in the Lombardy region of Italy. The results show that the proposed Vecchia-based MFGP closely matches exact multi-fidelity inference in controlled settings, while substantially outperforming standard single-fidelity spatio-temporal Gaussian processes in terms of predictive accuracy, correlation, and representation of local variability in realistic large-data scenarios.
format Preprint
id arxiv_https___arxiv_org_abs_2605_03693
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A new framework for non-stationary spatio-temporal data fusion of multi-fidelity models
Colombo, Pietro
Sigrist, Fabio
Miller, Claire
O'Donnell, Ruth
Yang, Xiaochen
Maranzano, Paolo
Computation
Methodology
We propose a new scalable framework for spatio-temporal data fusion with multi-fidelity Gaussian processes (MFGPs) that enables fully likelihood-based inference for both stationary and non-stationary fidelity integration. The framework is designed for environmental applications, where abundant but noisy low-fidelity data (e.g., satellite or reanalysis products) must be fused with sparse yet accurate high-fidelity in-situ observations to obtain high-resolution reconstructions. Our key methodological contribution is a decomposed multi-fidelity covariance formulation that allows the Vecchia approximation to be applied directly to the latent low-fidelity and discrepancy processes. Combined with a Woodbury-based reconstruction, this yields a numerically stable and computationally efficient evaluation of the joint marginal likelihood without ever forming the full multi-fidelity covariance matrix. In addition, we introduce a generalized least squares (GLS) mean-removal strategy with fidelity-specific offsets, preventing systematic biases from being absorbed into cross-fidelity dependence. We validate the proposed approach through extensive experiments on synthetic data and a large-scale real-world application to wind speed reconstruction in the Lombardy region of Italy. The results show that the proposed Vecchia-based MFGP closely matches exact multi-fidelity inference in controlled settings, while substantially outperforming standard single-fidelity spatio-temporal Gaussian processes in terms of predictive accuracy, correlation, and representation of local variability in realistic large-data scenarios.
title A new framework for non-stationary spatio-temporal data fusion of multi-fidelity models
topic Computation
Methodology
url https://arxiv.org/abs/2605.03693