Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian process, Part 1: Theory

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.

Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian Process, Part 2: Application to TRACE

“…Inverse UQ can be used to tackle the "lack of input uncertainty information" issue, which is a process to quantify the input uncertainties given experimental data. In our companion paper [5], we discussed the connection and difference between inverse UQ and calibration. In brief, deterministic calibration only results in point estimates of best-fit input parameters, while Bayesian calibration and inverse UQ target at quantifying the uncertainties in these input uncertainties.…”

“…Since measurement data are usually insufficient to inform us about the "true" or "exact" values of the calibration parameters, uncertainties in calibration parameters should be quantified to prevent over-confidence in the calibration process. Besides the subtle differences between Bayesian calibration and inverse UQ discussed in [5], they can be treated as the same concept in most cases.…”

“…In a companion paper [5], we presented the detailed theory and procedure to perform inverse UQ. We also proposed an improved modular Bayesian approach based on GP.…”

“…In this work, we have greatly improved the application in the following aspects: 1) GP is used to construct metamodel for TRACE code, which requires even less TRACE runs than SGSC used in [23]. Furthermore, as shown in our companion paper [5], GP metamodel provides Mean Square Error (MSE) of its prediction which is essentially the "code uncertainty" (see Section 2.3 in [5]).…”

Combining simulations and data with deep learning and uncertainty quantification for advanced energy modeling

“…18 Macfarland 19 developed and illustrated methods that support verification, validation, and inverse problems of computer models with emphasis on Bayesian inference and GPs. A rigorous GP-based inverse UQ framework was developed in a two-part series, 20,21 with a focus on nuclear thermal-hydraulics simulations. An uncertainty analysis of spent fuel isotopics and rod internal pressure was done in Bratton 22 and Bratton et al 23 A data-driven framework for boiling heat transfer, coupled with deep neural networks (DNN), was developed in Liu et al, 24 while another effort on wall boiling closure relations in computational fluid dynamics (CFD) multiphase flow solvers was demonstrated in Liu and Dinh.…”