| Abstract: | This work presents a parametric, non-intrusive, data-driven reduced-order model (ROM) for parametric multigroup radiation transport. Full-order models (FOMs) for radiation transport are often costly in terms of computational resources, due to the high dimensionality of the angular flux unknown and associated sweep operator. This burdensome cost may preclude the use of multi-query workflows, in which the problem is repeatedly evaluated for varying system parameters, for application to radiation transport. A ROM, which can be evaluated in a fraction of the time of the FOM, could provide a suitable substitute. The ROM is constructed in a data-driven way by utilizing a set of snapshots, previous evaluations of the FOM. From these snapshots, a parametric subspace of the solutions is discovered using the related methods of proper orthogonal decomposition and principle component analysis. The basis of this subspace is utilized in a non-intrusive way; this avoids complications which arise in intrusive ROMs due to the sweep operator. We explore three methods for learning the parametric response within this subspace: multivariate polynomial regression, Gaussian process regression (GPR), and multivariate adaptive regression splines (MARS). Differing constructions of the ROM are applied to a series of initial test problems. For 3D transport, speed up factors in excess of 20, 000 are observed, while achieving pointwise relative error under 1% throughout most of the domain. However, small regions of vanishing flux may result in regions of increased pointwise error. The ROM is then adapted to an atmospheric transport scenario, in which the FOM solution can vary by up to 26 orders of magnitude throughout the spatial domain. The non-intrusive nature of the ROM is utilized to formulate a four-component ROM construction for the atmospheric scenario. A speed up factor ranging from 5, 100× to 9, 700× is achieved. However, small regions of excessive error are present, either as a result of the variable height of the atmospheric source, or as an artifact due to co-locating the sources in the dataset. The electronic version of this dissertation is accessible from https://hdl.handle.net/1969.1/198543 |
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