Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference

TL;DR

This paper introduces a scalable Bayesian framework for uncertainty quantification and propagation in surrogate models, improving the reliability of predictions in complex simulation-based inference tasks.

Contribution

It presents three novel Bayesian methods for surrogate modeling that thoroughly quantify and propagate uncertainty, addressing computational challenges and validation.

Findings

Effective uncertainty propagation in surrogate models demonstrated in case studies

Enhanced reliability and safety in simulation-based inference tasks

Framework applicable to linear and nonlinear real-world scenarios

Abstract

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.