# Fit (Approximation)

A Fit is a mathematical model that is trained by data and is capable of predicting output response variables for a given set of input variables.

A Fit model can then be used as an inexpensive surrogate in lieu of an actual solver in another HyperStudy approach, it can be exported for use in an external application, or it can be used in its own right to conduct what-if analyses to learn more about the system being modeled.

Some simulations are computationally expensive which makes it impractical to rely on them exclusively for design studies. In these cases, the use of Fits leads to substantial savings of computational resources. Additionally, the use of a Fit can smooth out noisy functions.

When using approximations, the issue of a tradeoff between accuracy and efficiency is ever present. The challenge is how approximate the representation of the design space can be while remaining accurate enough. The answer to this question depends on the nature of the problem as well as the resources; type of output responses, number of design parameters, and how many runs can be afforded.