Inverse Uncertainty Quantification using the Modular Bayesian Approach based on Gaussian Process, Part 1: Theory

TL;DR

This paper develops a Bayesian framework using Gaussian Processes for inverse uncertainty quantification in nuclear reactor modeling, addressing model discrepancy and proposing an improved modular approach to enhance predictive accuracy.

Contribution

It introduces a systematic Bayesian inverse UQ method with Gaussian Process metamodels and proposes an improved modular approach to prevent overfitting and extrapolation errors.

Findings

Formulated inverse UQ using Bayesian analysis with Gaussian Process models.

Compared full and modular Bayesian approaches for inverse UQ.

Proposed an improved modular approach to avoid extrapolation of model discrepancy.

Abstract

In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. "Expert opinion" and "user self-evaluation" have been widely used to specify computer model input uncertainties in previous uncertainty, sensitivity and validation studies. Inverse Uncertainty Quantification (UQ) is the process to inversely quantify input uncertainties based on experimental data in order to more precisely quantify such ad-hoc specifications of the input uncertainty information. In this paper, we used Bayesian analysis to establish the inverse UQ formulation, with systematic and rigorously derived metamodels constructed by Gaussian Process (GP). Due to incomplete or inaccurate underlying physics, as well as numerical approximation errors, computer models always have discrepancy/bias in representing the realities, which can cause over-fitting if neglected in the inverse UQ process. The model discrepancy term is accounted for in our formulation through the "model updating equation". We provided a detailed introduction and comparison of the full and modular Bayesian approaches for inverse UQ, as well as pointed out their limitations when extrapolated to the validation/prediction domain. Finally, we proposed an improved modular Bayesian approach that can avoid extrapolating the model discrepancy that is learnt from the inverse UQ domain to the validation/prediction domain.