Model Structure Identification

In practice, determination of the model structure is the first problemthat a modeler has to deal with when modeling a complicatedphysical system. Model structure error is often the major cause ofmodel failure. Even a carefully calibrated model may produceunreliable results when it is used for prediction and decision-makingpurposes. In this chapter, an extended inverse problem (EIP) isformulated for identifying both the model structure and modelparameters using observation data and prior information. After themodel structure is parameterized, the solution of EIP becomes a minminoptimization problem. In the statistical framework, structureidentification requires estimation of both shape parameters andstatistical parameters. Statistical parameters are hyperparametersthat do not appear directly in the model but must be estimated duringthe inversion process. Model parameters and hyperparameters canbe estimated simultaneously or iteratively by hierarchical Bayesianinversion. Geostatistical inversion uses kriging and cokriging asparameterization for estimating a distributed parameter. The pilotpoint method is a flexible parameterization method for inversion thatcan decrease the model structure error of a geostatistical modeleffectively.