Meta modeling

The current section is dedicated to the building of an analytical approximation of the response of a given model. Such an approximation is commonly referred to as a response surface in the literature. This methodology is relevant if each model evaluation is time consuming. Indeed, once a response surface has been built up, the various propagation steps may be applied at a negligible cost. A special focus will be given to polynomial response surfaces.

General purpose surrogate models

• Taylor expansion
• Least squares polynomial response surface
• Sparse least squares metamodel
• Kriging
• Validation and cross validation of metamodels

Functional chaos

• Orthogonal polynomials
• Polynomial chaos basis
• Chaos basis enumeration strategies
• Functional Chaos Expansion
• Cross validation of PCE models