Problem
Research questions and friction points this paper is trying to address.
Uncertainty quantification in surrogate models
Propagation of surrogate-induced uncertainty
Bayesian inference with measurement data
Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference
🤖 AI Summary
In Bayesian inverse problems, surrogate models—constrained by limited simulation budgets and approximation errors—often induce biased parameter estimates and overconfident posterior distributions. To address this, we propose the first scalable Bayesian surrogate modeling framework that rigorously quantifies and propagates uncertainty across the entire pipeline: surrogate construction, posterior inference, and model validation. Methodologically, we integrate Gaussian process surrogate modeling, probabilistic programming, and posterior calibration techniques to design three novel Bayesian inversion algorithms, overcoming classical analytical assumptions and computational bottlenecks. We validate the framework on three real-world linear and nonlinear inverse problems. Results demonstrate substantial improvements in posterior calibration and parameter estimation reliability, leading to reduced decision risk. The framework establishes a new paradigm for robust uncertainty quantification under resource constraints.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Bayesian surrogate modeling
Uncertainty quantification
Scalable computational framework
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