# Defining Inverse Problems

An inverse problem is a collection of experiments which define a multi-simulation optimization problem. The solution to an inverse problem are the "good parameters" which make the simulations simultaneously fit their respective data sufficiently well.

## Constructing InverseProblems

JuliaSimModelOptimizer.InverseProblemType
InverseProblem(experiments, search_space)

The InverseProblem represents the problem of finding some parameters and/or initial conditions that best fit what we know about our system(s). The known information is expressed in the form of an Experiment, or a collection of such objects. The search_space is a Vector of pairs. Each pair consists of a parameter or initial condition that we need to find and its lower and upper bounds. If the keys of the pairs are symbolic variables, they are assumed to be part of one of the models in the inverse problem. If they are a String, then they are assumed to represent a description and it is required for that description to be unique across models. The value can be:

• a tuple of 2 numbers representing lower and upper bounds
• a tuple of 3 numbers, where the first will be the initial guess and the last 2 will be lower and upper bounds
• a tuple of 3 elements, where the first 2 are numbers and represent lower and upper bounds and the last element is a Symbol, specifying a model transformation (:log, :log10 or :identity)
• a tuple of 4 elements, where the first number is the initial guess, the last 2 will be lower and upper bounds and the last is a Symbol, specifying a model transformation (:log, :log10 or :identity)
• a distribution (<:Distribuitions.Sampleable)
• a tuple of a distribution (<:Distribuitions.Sampleable) and a Symbol, specifying a model transformation (:log, :log10 or :identity)

Each experiment defines an error function that can expresses how well a certain combination of search_space values fits the corresponding data or how well does that particular configuration match a certain objective.

All the experiments are taken into account when finding the values in the search_space, their individual contributions being summed when computing the overall metric for how good a particular combination of search_space values is. This overall metric can be obtained by calling objective.

Positional arguments

• experiments: the experiments defining the inverse problem
• search_space: the search space for the inverse problem representing the unknown parameters or initial conditions to be tuned
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