Gray, Ander 
ORCID: 0000-0002-1585-0900
(2022)
Correlated uncertainty arithmetic with application to fusion neutronics.
Doctor of Philosophy thesis, University of Liverpool.
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Abstract
his thesis advances the idea of automatic and rigorous uncertainty propagation for computational science. The aim is to replace the deterministic arithmetic and logical operations composing a function or a computer program with their uncertain equivalents. In this thesis, uncertain computer variables are labelled uncertain numbers, which may be probability distributions, intervals, probability boxes, and possibility distributions. The individual models of uncertainty are surveyed in the context of imprecise probability theory, and their individual arithmetic described and developed, with new results presented in each arithmetic. The presented arithmetic framework allows random variables to be imprecisely characterised or partially defined. It is a common situation that input random variables are unknown or that only certain characteristics of the inputs are known. How uncertain numbers can be rigorously represented by a finite numerical discretisation is described. Further, it is shown how arithmetic operations are computed by numerical convolution, accounting for both the error from the input's discretisation and from the numerical integration, yielding guaranteed bounds on computed uncertain numbers. One of the central topics of this thesis is stochastic dependency. Considering complex dependencies amongst uncertain numbers is necessary, as it plays a key role in operations. An arithmetic operation between two uncertain numbers is a function not only of the input numbers, but also how they are correlated. This is often more important than the marginal information. In the presented arithmetic, dependencies between uncertain numbers may also be partially defined or missing entirely. A major proposition of this thesis are methods to propagate dependence information through functions alongside marginal information. The long-term goal is to solve probabilistic problems with partial knowledge about marginal distributions and dependencies using algorithms which were written deterministically. The developed arithmetic frameworks can be used individually, or may be combined into a larger uncertainty computing framework. We present an application of the developed method to a radiation transport algorithm for nuclear fusion neutronics problems.
| Item Type: | Thesis (Doctor of Philosophy) |
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| Divisions: | Faculty of Science and Engineering > School of Engineering |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 17 Aug 2023 14:21 |
| Last Modified: | 17 Aug 2023 14:22 |
| DOI: | 10.17638/03170585 |
| Supervisors: |
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| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3170585 |
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