### 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.

Original language | English (US) |
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Pages (from-to) | 1747-1764 |

Number of pages | 18 |

Journal | Journal of Mathematical Chemistry |

Volume | 50 |

Issue number | 7 |

DOIs | |

State | Published - Aug 1 2012 |

### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Applied Mathematics

### Keywords

- D-MORPH regression
- Least-squares regression
- Regularization
- Ridge regression

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## Cite this

*Journal of Mathematical Chemistry*,

*50*(7), 1747-1764. https://doi.org/10.1007/s10910-012-0004-z