# Bayesian Surrogate Analysis and Uncertainty Propagation

arXiv: https://arxiv.org/abs/2101.04038 · HTML: https://mlsanity.com/paper/2101.04038/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2021.

## Built on by (most cited first, 10 of 10)

- [Sources of Uncertainty in 3D Scene Reconstruction](https://mlsanity.com/paper/2409.06407/) (2024)
- [Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference](https://mlsanity.com/paper/2312.05153/) (2023)
- [Deep Polynomial Chaos Expansion](https://mlsanity.com/paper/2507.21273/) (2025)
- [Robust Bayesian Target Value Optimization](https://mlsanity.com/paper/2301.04344/) (2023)
- [Stochastic Modeling of Inhomogeneities in the Aortic Wall and Uncertainty Quantification using a Bayesian Encoder-Decoder Surrogate](https://mlsanity.com/paper/2202.10244/) (2022)
- [A connection between probability, physics and neural networks](https://mlsanity.com/paper/2209.12737/) (2022)
- [Generalized Early Stopping in Evolutionary Direct Policy Search](https://mlsanity.com/paper/2308.03574/) (2023)
- [CameraVDP: Perceptual Display Assessment with Uncertainty Estimation via Camera and Visual Difference Prediction](https://mlsanity.com/paper/2509.08947/) (2025)
- [Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy](https://mlsanity.com/paper/2412.11875/) (2024)
- [Multi-level informed optimization via decomposed Kriging for large design problems under uncertainty](https://mlsanity.com/paper/2510.07904/) (2025)

## Abstract (arXiv)

The quantification of uncertainties of computer simulations due to input parameter uncertainties is paramount to assess a model's credibility. For computationally expensive simulations, this is often feasible only via surrogate models that are learned from a small set of simulation samples. The surrogate models are commonly chosen and deemed trustworthy based on heuristic measures, and substituted for the simulation in order to approximately propagate the simulation input uncertainties to the simulation output. In the process, the contribution of the uncertainties of the surrogate itself to the simulation output uncertainties are usually neglected. In this work, we specifically address the case of doubtful surrogate trustworthiness, i.e. non-negligible surrogate uncertainties. We find that Bayesian probability theory yields a natural measure of surrogate trustworthiness, and that surrogate uncertainties can easily be included in simulation output uncertainties. For a Gaussian likelihood for the simulation data, with unknown surrogate variance and given a generalized linear surrogate model, the resulting formulas reduce to simple matrix multiplications. The framework contains Polynomial Chaos Expansions as a special case, and is easily extended to Gaussian Process Regression. Additionally, we show a simple way to implicitly include spatio-temporal correlations. Lastly, we demonstrate a numerical example where surrogate uncertainties are in part negligible and in part non-negligible.