%0 Journal Article %1 springerlink:10.1007/s10910-012-0004-z %A Li, Genyuan %A Rey-de Castro, Roberto %A Rabitz, Herschel %D 2012 %I Springer Netherlands %J Journal of Mathematical Chemistry %K analysis data fit least mathematics squares %N 7 %P 1747-1764 %R 10.1007/s10910-012-0004-z %T D-MORPH regression for modeling with fewer unknown parameters than observation data %U http://dx.doi.org/10.1007/s10910-012-0004-z %V 50 %X D-MORPH regression is a procedure for the treatment of a model prescribed as a linear superposition of basis functions with less observation data than the number of expansion parameters. In this case, there is an infinite number of solutions exactly fitting the data. D-MORPH regression provides a practical systematic means to search over the solutions seeking one with desired ancillary properties while preserving fitting accuracy. This paper extends D-MORPH regression to consider the common case where there is more observation data than unknown parameters. This situation is treated by utilizing a proper subset of the normal equation of least-squares regression to judiciously reduce the number of linear algebraic equations to be less than the number of unknown parameters, thereby permitting application of D-MORPH regression. As a result, no restrictions are placed on model complexity, and the model with the best prediction accuracy can be automatically and efficiently identified. Ignition data for a H 2 /air combustion model as well as laboratory data for quantum-control-mechanism identification are used to illustrate the method.

@article{springerlink:10.1007/s10910-012-0004-z, abstract = {D-MORPH regression is a procedure for the treatment of a model prescribed as a linear superposition of basis functions with less observation data than the number of expansion parameters. In this case, there is an infinite number of solutions exactly fitting the data. D-MORPH regression provides a practical systematic means to search over the solutions seeking one with desired ancillary properties while preserving fitting accuracy. This paper extends D-MORPH regression to consider the common case where there is more observation data than unknown parameters. This situation is treated by utilizing a proper subset of the normal equation of least-squares regression to judiciously reduce the number of linear algebraic equations to be less than the number of unknown parameters, thereby permitting application of D-MORPH regression. As a result, no restrictions are placed on model complexity, and the model with the best prediction accuracy can be automatically and efficiently identified. Ignition data for a H 2 /air combustion model as well as laboratory data for quantum-control-mechanism identification are used to illustrate the method.}, added-at = {2012-08-11T04:42:07.000+0200}, affiliation = {Department of Chemistry, Princeton University, Princeton, NJ 08544, USA}, author = {Li, Genyuan and Rey-de Castro, Roberto and Rabitz, Herschel}, biburl = {https://www.bibsonomy.org/bibtex/20e1f50fb5b6489a6399ecc4bc898240e/drmatusek}, description = {Journal of Mathematical Chemistry, Volume 50, Number 7 - SpringerLink}, doi = {10.1007/s10910-012-0004-z}, interhash = {2eb06105cf1c58b31fcdbfadd0c0c804}, intrahash = {0e1f50fb5b6489a6399ecc4bc898240e}, issn = {0259-9791}, journal = {Journal of Mathematical Chemistry}, keyword = {Chemistry and Materials Science}, keywords = {analysis data fit least mathematics squares}, month = aug, number = 7, pages = {1747-1764}, publisher = {Springer Netherlands}, timestamp = {2012-10-10T05:14:14.000+0200}, title = {D-MORPH regression for modeling with fewer unknown parameters than observation data}, url = {http://dx.doi.org/10.1007/s10910-012-0004-z}, volume = 50, year = 2012 }