# Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities

arXiv: https://arxiv.org/abs/2006.16728 · HTML: https://mlsanity.com/paper/2006.16728/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2020.

## Built on by (most cited first, 24 of 24)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed](https://mlsanity.com/paper/2203.09179/) (2022)
- [Multi-fidelity Hierarchical Neural Processes](https://mlsanity.com/paper/2206.04872/) (2022)
- [Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling](https://mlsanity.com/paper/2402.18846/) (2024)
- [Multi-fidelity Bayesian Optimization: A Review](https://mlsanity.com/paper/2311.13050/) (2023)
- [Disentangled Multi-Fidelity Deep Bayesian Active Learning](https://mlsanity.com/paper/2305.04392/) (2023)
- [A Latent Variable Approach for Non-Hierarchical Multi-Fidelity Adaptive Sampling](https://mlsanity.com/paper/2310.03298/) (2023)
- [Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling](https://mlsanity.com/paper/2111.14008/) (2021)
- [Multi-Fidelity Methods for Optimization: A Survey](https://mlsanity.com/paper/2402.09638/) (2024)
- [Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization](https://mlsanity.com/paper/2109.09261/) (2021)
- [Multi-fidelity Monte Carlo: a pseudo-marginal approach](https://mlsanity.com/paper/2210.01534/) (2022)
- [Multifidelity linear regression for scientific machine learning from scarce data](https://mlsanity.com/paper/2403.08627/) (2024)
- [Non-Myopic Multifidelity Bayesian Optimization](https://mlsanity.com/paper/2207.06325/) (2022)
- [MFBind: a Multi-Fidelity Approach for Evaluating Drug Compounds in Practical Generative Modeling](https://mlsanity.com/paper/2402.10387/) (2024)
- [Uncertainty-aware multi-fidelity surrogate modeling with noisy data](https://mlsanity.com/paper/2401.06447/) (2024)
- [Combining additivity and active subspaces for high-dimensional Gaussian process modeling](https://mlsanity.com/paper/2402.03809/) (2024)
- [MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning](https://mlsanity.com/paper/2410.11226/) (2024)
- [Efficient Controller Learning from Human Preferences and Numerical Data Via Multi-Modal Surrogate Models](https://mlsanity.com/paper/2603.24138/) (2026)
- [Physics-informed reinforcement learning via probabilistic co-adjustment functions](https://mlsanity.com/paper/2309.05404/) (2023)
- [Gradient-enhanced deep Gaussian processes for multifidelity modelling](https://mlsanity.com/paper/2402.16059/) (2024)
- [MAST: A Multi-fidelity Augmented Surrogate model via Spatial Trust-weighting](https://mlsanity.com/paper/2602.20974/) (2026)
- [Optimization-Embedded Active Multi-Fidelity Surrogate Learning for Multi-Condition Airfoil Shape Optimization](https://mlsanity.com/paper/2603.17057/) (2026)
- [Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data](https://mlsanity.com/paper/2603.22050/) (2026)
- [MF-SCBO : Multi-fidelity Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2609.29941/) (2026)

## Abstract (arXiv)

The design process of complex systems such as new configurations of aircraft or launch vehicles is usually decomposed in different phases which are characterized for instance by the depth of the analyses in terms of number of design variables and fidelity of the physical models. At each phase, the designers have to compose with accurate but computationally intensive models as well as cheap but inaccurate models. Multi-fidelity modeling is a way to merge different fidelity models to provide engineers with accurate results with a limited computational cost. Within the context of multi-fidelity modeling, approaches relying on Gaussian Processes emerge as popular techniques to fuse information between the different fidelity models. The relationship between the fidelity models is a key aspect in multi-fidelity modeling. This paper provides an overview of Gaussian process-based multi-fidelity modeling techniques for variable relationship between the fidelity models (e.g., linearity, non-linearity, variable correlation). Each technique is described within a unified framework and the links between the different techniques are highlighted. All the approaches are numerically compared on a series of analytical test cases and four aerospace related engineering problems in order to assess their benefits and disadvantages with respect to the problem characteristics.