# Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference

arXiv: https://arxiv.org/abs/2312.05153 · HTML: https://mlsanity.com/paper/2312.05153/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 102 references that are in the map.
- First posted on arXiv 8 Dec 2023.

## Builds on (most cited first, 30 of 30)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Simulation Intelligence: Towards a New Generation of Scientific Methods](https://mlsanity.com/paper/2112.03235/) (2021)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison](https://mlsanity.com/paper/2103.10522/) (2021)
- [A SIDARTHE Model of COVID-19 Epidemic in Italy](https://mlsanity.com/paper/2003.09861/) (2020)
- [Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity](https://mlsanity.com/paper/2211.02383/) (2022)
- [Automatic Reparameterisation of Probabilistic Programs](https://mlsanity.com/paper/1906.03028/) (2019)
- [Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy](https://mlsanity.com/paper/2209.02439/) (2022)
- [Improved uncertainty quantification for neural networks with Bayesian last layer](https://mlsanity.com/paper/2302.10975/) (2023)
- [Bayesian Surrogate Analysis and Uncertainty Propagation](https://mlsanity.com/paper/2101.04038/) (2021)
- [Projective Inference in High-dimensional Problems: Prediction and Feature Selection](https://mlsanity.com/paper/1810.02406/) (2018)
- [Detecting and diagnosing prior and likelihood sensitivity with power-scaling](https://mlsanity.com/paper/2107.14054/) (2021)
- [Discussion of Big Bayes Stories and BayesBag](https://mlsanity.com/paper/1405.4977/) (2014)
- [Better together? Statistical learning in models made of modules](https://mlsanity.com/paper/1708.08719/) (2017)
- [Deep Surrogate for Direct Time Fluid Dynamics](https://mlsanity.com/paper/2112.10296/) (2021)
- [A fully Bayesian sparse polynomial chaos expansion approach with joint priors on the coefficients and global selection of terms](https://mlsanity.com/paper/2204.06043/) (2022)
- [Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models](https://mlsanity.com/paper/1909.01648/) (2019)
- [Meta-analysis of Bayesian analyses](https://mlsanity.com/paper/1904.04484/) (2019)
- [Penalised t-walk MCMC](https://mlsanity.com/paper/2012.02293/) (2020)
- [Surrogate Ensemble Forecasting for Dynamic Climate Impact Models](https://mlsanity.com/paper/2204.05795/) (2022)

## Built on by (most cited first, 4 of 4)

- [SMRS: advocating a unified reporting standard for surrogate models in the artificial intelligence era](https://mlsanity.com/paper/2502.06753/) (2025)
- [Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models](https://mlsanity.com/paper/2505.08683/) (2025)
- [Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy](https://mlsanity.com/paper/2412.11875/) (2024)
- [Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates](https://mlsanity.com/paper/2608.11435/) (2026)

## Abstract (arXiv)

Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to predictions, inference, and subsequent decision-relevant quantities. However, quantifying and then propagating the uncertainty of surrogates is usually limited to special analytic cases or is otherwise computationally very expensive. In this paper, we propose a framework enabling a scalable, Bayesian approach to surrogate modeling with thorough uncertainty quantification, propagation, and validation. Specifically, we present three methods for Bayesian inference with surrogate models given measurement data. This is a task where the propagation of surrogate uncertainty is especially relevant, because failing to account for it may lead to biased and/or overconfident estimates of the parameters of interest. We showcase our approach in three detailed case studies for linear and nonlinear real-world modeling scenarios. Uncertainty propagation in surrogate models enables more reliable and safe approximation of expensive simulators and will therefore be useful in various fields of applications.