A new framework for non-stationary spatio-temporal data fusion of multi-fidelity models
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913090748022784 |
|---|---|
| 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 |