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

2026-05-05

AI Summary

This study addresses the challenge of fusing sparse, high-accuracy in-situ observations with massive, low-accuracy remote sensing or reanalysis data for high-resolution reconstruction of nonstationary spatiotemporal fields. The authors propose a scalable multi-fidelity Gaussian process framework that innovatively applies the Vecchia approximation directly to both low-fidelity and bias latent processes. By integrating the Woodbury matrix identity with a generalized least squares detrending strategy featuring fidelity-specific offsets, the method enables full likelihood inference while maintaining numerical stability. Experiments on synthetic data and a real-world wind speed reconstruction task in Lombardy, Italy, demonstrate that the proposed approach significantly outperforms single-fidelity models, achieving superior predictive accuracy and more faithfully capturing spatial correlations and local variability.

Abstract

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.

Problem

• spatio-temporal data fusion
• multi-fidelity models
• non-stationary processes
• Gaussian processes
• environmental monitoring

Innovation

• multi-fidelity Gaussian processes
• Vecchia approximation
• non-stationary spatio-temporal fusion
• Woodbury-based reconstruction
• generalized least squares mean removal