First Advisor

Dacian N. Daescu

Term of Graduation

Fall 2009

Date of Publication


Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Mathematical Sciences






Atmospheric chemistry, Chemical kinetics -- Mathematical models, Dimension reduction (Statistics), Orthogonal decompositions, Academic theses



Physical Description

1 online resource (ix, 254 pages)


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.


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