Sponsor
Portland State University. Department of Mathmatics
First Advisor
Dacian N. Daescu
Term of Graduation
Fall 2009
Date of Publication
10-15-2009
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.) in Mathematical Sciences
Department
Mathematics
Language
English
Subjects
Atmospheric chemistry, Chemical kinetics -- Mathematical models, Dimension reduction (Statistics), Orthogonal decompositions, Academic theses
DOI
10.15760/etd.7854
Physical Description
1 online resource (ix, 254 pages)
Abstract
Many tasks of simulation, optimization and control can be performed more efficiently if the intermediate complexity of the numerical model is reduced. In our work, we investigate model reduction, as applied to reaction-transport systems of atmospheric chemistry. We use a Proper Orthogonal Decomposition-based approach to extract information from a set of model observations, and to project the model equations onto a reduced order space chosen in such a way that the essential model behavior is preserved in the solution of the reduced version. We examine and improve many features of the method. In particular, we show how to measure sensitivities of the model reduction process, and use the results to select the placement and weighting of observations to best reproduce specific events in the full model behavior; we also develop novel techniques allowing to take into account multiple events We show how to construct reduced models to replace the full model in iterative parameter optimization procedures so that fewer steps and lower computational budget are needed. The result of the study is a more complete understanding of how to perform tasks of simulation and optimization of nonlinear models using model reduction tools.
Rights
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Persistent Identifier
https://archives.pdx.edu/ds/psu/37836
Recommended Citation
Roderick, Oleg Edward, "Model Reduction for Simulation, Optimization and Control" (2009). Dissertations and Theses. Paper 5984.
https://doi.org/10.15760/etd.7854
Comments
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