Computational models that describe complex physical phenomena tend to be computationally expensive and time consuming. Partial differential equation (PDE) based models in particular produce spatio-temporal data sets in high dimensional output spaces. Repeated calls of computer models to perform tasks such as sensitivity analysis, uncertainty quantification and design optimization can become computationally infeasible as a result. While constructing an emulator is one solution to approximate the outcome of expensive computer models, it is not always capable of dealing with high-dimensional data sets. To deal with high-dimensional data, in this thesis emulation strategies (Gaussian processes (GPs), artificial neural networks (ANNs) and support vector machines (SVMs)) are combined with linear and non-linear dimensionality reduction techniques (kPCA, Isomap and diffusion maps) to develop efficient emulators. For sensitivity analysis (variance based), a probabilistic framework is developed to account for the emulator uncertainty and the method is extended to multivariate outputs, with a derivation of new semi-analytical results for performing rapid sensitivity analysis of univariate or multivariate outputs. The developed emulators are also used to extend reduced order models (ROMs) based on proper orthogonal decomposition to parameter-dependent PDEs, including an extension of the discrete empirical interpolation method for non-linear problems PDE systems.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:767147 |
| Date | January 2018 |
| Creators | Triantafyllidis, Vasileios |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/114588/ |
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