# Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulations

arXiv: https://arxiv.org/abs/2104.03743 · HTML: https://mlsanity.com/paper/2104.03743/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 8 Apr 2021.

## Builds on (most cited first, 8 of 8)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1811.00755/) (2018)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Uniform Error and Posterior Variance Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/2101.05328/) (2021)

## Built on by (most cited first, 8 of 8)

- [Multi-Resolution Active Learning of Fourier Neural Operators](https://mlsanity.com/paper/2309.16971/) (2023)
- [Infinite-Fidelity Coregionalization for Physical Simulation](https://mlsanity.com/paper/2207.00678/) (2022)
- [GAR: Generalized Autoregression for Multi-Fidelity Fusion](https://mlsanity.com/paper/2301.05729/) (2023)
- [Diffusion-Generative Multi-Fidelity Learning for Physical Simulation](https://mlsanity.com/paper/2311.05606/) (2023)
- [FIRE: Multi-fidelity Regression with Distribution-conditioned In-context Learning using Tabular Foundation Models](https://mlsanity.com/paper/2601.22371/) (2026)
- [Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems](https://mlsanity.com/paper/2212.02250/) (2022)
- [COMPOL: A Unified Neural Operator Framework for Scalable Multi-Physics Simulations](https://mlsanity.com/paper/2501.17296/) (2025)
- [Prediction of liquid fuel properties using machine learning models with Gaussian processes and probabilistic conditional generative learning](https://mlsanity.com/paper/2110.09360/) (2021)

## Abstract (arXiv)

Challenges in multi-fidelity modeling relate to accuracy, uncertainty estimation and high-dimensionality. A novel additive structure is introduced in which the highest fidelity solution is written as a sum of the lowest fidelity solution and residuals between the solutions at successive fidelity levels, with Gaussian process priors placed over the low fidelity solution and each of the residuals. The resulting model is equipped with a closed-form solution for the predictive posterior, making it applicable to advanced, high-dimensional tasks that require uncertainty estimation. Its advantages are demonstrated on univariate benchmarks and on three challenging multivariate problems. It is shown how active learning can be used to enhance the model, especially with a limited computational budget. Furthermore, error bounds are derived for the mean prediction in the univariate case.