# Inverse Methods

## Abstract

A broad description of inverse methods (introduced in Sect. 1.3.3) is that they pertain to the case when the system under study already exists, and one uses measured or observed system behavior to aid in the model building. The three types of inverse problems were classified as: (i) calibration of white-box models (which can be either relatively simple or complex-coupled simulation models) which requires that one selectively manipulate certain parameters of the model to fit observed data. Monte Carlo methods which are powerful random sampling techniques are described along with regional sensitivity analyses as a means of reducing model order of complex simulation models; (ii) model selection and parameter estimation involving positing either black-box or grey-box models, and using regression methods to identify model parameters based on some criterion of error minimization (the least squares regression method and the maximum likelihood method being the most popular); and (iii) control problems where input states and/or boundary conditions are inferred from knowledge of output states and model parameters. This chapter elaborates on these methods and illustrates their approach with case study examples. Local polynomial regression methods are also briefly described as well as the multi-layer perceptron approach, which is a type of neural network modeling method that is widely used in modeling non-linear or complex phenomena. Further, the selection of a grey-box model based more on policy decisions rather than on how well a model fits the data is illustrated in the framework of dose-response models. Finally, variable model formulation and compartmental modeling appropriate for describing dynamic behavior of linear systems are introduced along with a discussion of certain identifiability issues in practice.

## Keywords

Hide Layer Deep Space Regressor Variable Utility Bill Identifiability Issue## Supplementary material

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