777 research outputs found
Inverse Uncertainty Quantification using the Modular Bayesian Approach based on Gaussian Process, Part 1: Theory
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.Comment: 27 pages, 10 figures, articl
Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial
On top of machine learning models, uncertainty quantification (UQ) functions
as an essential layer of safety assurance that could lead to more principled
decision making by enabling sound risk assessment and management. The safety
and reliability improvement of ML models empowered by UQ has the potential to
significantly facilitate the broad adoption of ML solutions in high-stakes
decision settings, such as healthcare, manufacturing, and aviation, to name a
few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods
for ML models with a particular focus on neural networks and the applications
of these UQ methods in tackling engineering design as well as prognostics and
health management problems. Toward this goal, we start with a comprehensive
classification of uncertainty types, sources, and causes pertaining to UQ of ML
models. Next, we provide a tutorial-style description of several
state-of-the-art UQ methods: Gaussian process regression, Bayesian neural
network, neural network ensemble, and deterministic UQ methods focusing on
spectral-normalized neural Gaussian process. Established upon the mathematical
formulations, we subsequently examine the soundness of these UQ methods
quantitatively and qualitatively (by a toy regression example) to examine their
strengths and shortcomings from different dimensions. Then, we review
quantitative metrics commonly used to assess the quality of predictive
uncertainty in classification and regression problems. Afterward, we discuss
the increasingly important role of UQ of ML models in solving challenging
problems in engineering design and health prognostics. Two case studies with
source codes available on GitHub are used to demonstrate these UQ methods and
compare their performance in the life prediction of lithium-ion batteries at
the early stage and the remaining useful life prediction of turbofan engines
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