# Data Fusion with Latent Map Gaussian Processes

arXiv: https://arxiv.org/abs/2112.02206 · HTML: https://mlsanity.com/paper/2112.02206/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 4 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors](https://mlsanity.com/paper/1806.07504/) (2018)
- [Latent Map Gaussian Processes for Mixed Variable Metamodeling](https://mlsanity.com/paper/2102.03935/) (2021)
- [Kernel Interpolation for Scalable Online Gaussian Processes](https://mlsanity.com/paper/2103.01454/) (2021)
- [A theoretical framework for calibration in computer models: parametrization, estimation and convergence properties](https://mlsanity.com/paper/1508.07155/) (2015)
- [Efficient Calibration for Imperfect Computer Models](https://mlsanity.com/paper/1507.07280/) (2015)
- [Patchwork Kriging for Large-scale Gaussian Process Regression](https://mlsanity.com/paper/1701.06655/) (2017)
- [Calibrating a large computer experiment simulating radiative shock hydrodynamics](https://mlsanity.com/paper/1410.3293/) (2014)

## Built on by (most cited first, 16 of 16)

- [Multi-Fidelity Cost-Aware Bayesian Optimization](https://mlsanity.com/paper/2211.02732/) (2022)
- [Operator Learning with Gaussian Processes](https://mlsanity.com/paper/2409.04538/) (2024)
- [Multi-fidelity wavelet neural operator with application to uncertainty quantification](https://mlsanity.com/paper/2208.05606/) (2022)
- [A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Sampling](https://mlsanity.com/paper/2310.03298/) (2023)
- [Probabilistic Neural Data Fusion for Learning from an Arbitrary Number of Multi-fidelity Data Sets](https://mlsanity.com/paper/2301.13271/) (2023)
- [Practical multi-fidelity machine learning: fusion of deterministic and Bayesian models](https://mlsanity.com/paper/2407.15110/) (2024)
- [Interpretable Multi-Source Data Fusion Through Latent Variable Gaussian Process](https://mlsanity.com/paper/2402.04146/) (2024)
- [Constrained multi-fidelity Bayesian optimization with automatic stop condition](https://mlsanity.com/paper/2503.01126/) (2025)
- [On the Effects of Heterogeneous Errors on Multi-fidelity Bayesian Optimization](https://mlsanity.com/paper/2309.02771/) (2023)
- [Heterogenous Multi-Source Data Fusion Through Input Mapping and Latent Variable Gaussian Process](https://mlsanity.com/paper/2407.11268/) (2024)
- [Unsupervised Anomaly Detection via Nonlinear Manifold Learning](https://mlsanity.com/paper/2306.09441/) (2023)
- [Multi-fidelity Design of Porous Microstructures for Thermofluidic Applications](https://mlsanity.com/paper/2310.18505/) (2023)
- [Characterising harmful data sources when constructing multi-fidelity surrogate models](https://mlsanity.com/paper/2403.08118/) (2024)
- [A preliminary data fusion study to assess the feasibility of Foundation Process-Property Models in Laser Powder Bed Fusion](https://mlsanity.com/paper/2503.16667/) (2025)
- [Should We Simultaneously Calibrate Multiple Computer Models?](https://mlsanity.com/paper/2505.18176/) (2025)
- [On the Brittleness of Maximum Likelihood Estimation for Gaussian Process Hyperparameter Optimization](https://mlsanity.com/paper/2608.13793/) (2026)

## Abstract (arXiv)

Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate data fusion. In our approach, we convert data fusion into a latent space learning problem where the relations among different data sources are automatically learned. This conversion endows our approach with attractive advantages such as increased accuracy, reduced costs, flexibility to jointly fuse any number of data sources, and ability to visualize correlations between data sources. This visualization allows the user to detect model form errors or determine the optimum strategy for high-fidelity emulation by fitting LMGP only to the subset of the data sources that are well-correlated. We also develop a new kernel function that enables LMGPs to not only build a probabilistic multi-fidelity surrogate but also estimate calibration parameters with high accuracy and consistency. The implementation and use of our approach are considerably simpler and less prone to numerical issues compared to existing technologies. We demonstrate the benefits of LMGP-based data fusion by comparing its performance against competing methods on a wide range of examples.