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

TL;DR

This paper introduces a scalable, likelihood-based multi-fidelity Gaussian process framework for non-stationary spatio-temporal data fusion, improving environmental data reconstruction accuracy.

Contribution

It presents a novel decomposed covariance formulation and efficient inference method for multi-fidelity Gaussian processes, applicable to large-scale environmental data.

Findings

Vecchia-based MFGP closely matches exact inference in synthetic tests.

Outperforms single-fidelity Gaussian processes in real-world wind speed data.

Provides high-resolution environmental reconstructions with improved accuracy.

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.