There are several types of metamodel: linear regression, splines, neural networks, etc.
This paper distinguishes between fitting and validating a metamodel.
A model conforms to its metamodel in the way that a computer program conforms to the grammar of the programming language in which it is written.
Various types of metamodels include polynomial equations, neural network, Kriging, etc.
Metamodel can be a mathematical relation or algorithm representing input and output relations.
This process includes classic design of experiments (DOE) and measuring fit through standard measures such as -square and cross-validation statistics.Classic design of experiments (DOE) is summarized, including standard measures of fit such as the R-square coefficient and cross-validation measures.This DOE is extended to sequential or stagewise DOE.Metamodels are of many types and have diverse applications.A thorough discussion is presented in the following text.Thus metamodeling or meta-modeling is the analysis, construction and development of the frames, rules, constraints, models and theories applicable and useful for modeling a predefined class of problems.