# Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion

arXiv: https://arxiv.org/abs/1812.06467 · HTML: https://mlsanity.com/paper/1812.06467/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2018.

## Built on by (most cited first, 6 of 6)

- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data](https://mlsanity.com/paper/2205.13545/) (2022)
- [Learning the Hodgkin-Huxley Model with Operator Learning Techniques](https://mlsanity.com/paper/2406.02173/) (2024)
- [Multi-fidelity Gaussian process surrogate modeling for regression problems in physics](https://mlsanity.com/paper/2404.11965/) (2024)
- [Non-Myopic Multifidelity Bayesian Optimization](https://mlsanity.com/paper/2207.06325/) (2022)
- [A joint optimization approach to identifying sparse dynamics using least squares kernel collocation](https://mlsanity.com/paper/2511.18555/) (2025)

## Abstract (arXiv)

In statistical modeling with Gaussian Process regression, it has been shown that combining (few) high-fidelity data with (many) low-fidelity data can enhance prediction accuracy, compared to prediction based on the few high-fidelity data only. Such information fusion techniques for multifidelity data commonly approach the high-fidelity model fh(t) as a function of two variables (t,y), and then using fl(t) as the y data. More generally, the high-fidelity model can be written as a function of several variables (t,y1,y2....); the low-fidelity model fl and, say, some of its derivatives, can then be substituted for these variables. In this paper, we will explore mathematical algorithms for multifidelity information fusion that use such an approach towards improving the representation of the high-fidelity function with only a few training data points. Given that fh may not be a simple function -- and sometimes not even a function -- of fl, we demonstrate that using additional functions of t, such as derivatives or shifts of fl, can drastically improve the approximation of fh through Gaussian Processes. We also point out a connection with "embedology" techniques from topology and dynamical systems.