Integration
Integration of Prior Knowledge, Inverse UQ and Quantitative Validation
The objective of this research is to develop a framework that integrates prior knowledge, inverse UQ results from the calibration domain, and quantitative validation results from the validation domain, to improve results in the prediction domain where there is little experimental data available. This framework is comprehensive in the sense that it simultaneously accounts for all major sources of quantifiable uncertainties in M&S, i.e., uncertainties from parameters, experiment, model, and code. It combines M&S, experimentation, and scientific machine learning into a unified approach to improve the predictive capabilities of computational models, with robustly established uncertainty estimations for safety parameters of interest thus enabling trustworthy regulatory licensing calculations. By bridging the gap between model and data, this framework can reduce the reliance on expensive measurement data for validation, which is especially important for advanced nuclear reactor M&S development.
Framework to enhance predictive capabilities of computer models.
The above framework consists of three major steps: (1) Calibration (herein also referred to as inverse UQ), which is the process to inversely quantify the parameter uncertainties based on experimental data. (2) Validation, which is the step to quantitatively evaluate the accuracy of the calibrated model using validation data. We will develop a quantitative validation metric called the Bayes factor based on Bayesian hypothesis testing. (3) Prediction, which combines prior knowledge, inverse UQ and quantitative validation to simulate the Quantities-of-Interests (QoIs) with established uncertainty in the prediction domain. The predictions will be made by averaging the simulations from the prior and posterior models, weighted by the probabilities that each model is more accurate which is indicated based on the Bayes factor.
The most important innovation in this work is that all steps are Bayesian, which is a natural way to integrate all information available, including prior knowledge, calibration data and validation data, while accounting for uncertainties. Another significant novelty is that the integrated framework incorporates uncertainties from four major sources, which are listed in the rows of the Figure below: (1) model uncertainty, due to missing/inaccurate underlying physics in the computer models, as well as numerical approximation errors; (2) experiment uncertainty, due to measurement noise; (3) code uncertainty, due to emulation of computationally prohibitive codes with surrogate models. Quantifying their approximation uncertainties is important especially when they are extrapolated outside of the training domain; (4) parameter uncertainty, due to ignorance in the exact values of input parameters (epistemic) or randomness (aleatory). The four sources of uncertainties include the most, if not all, of the quantifiable uncertainties that should be considered in all M&S problems.