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About Fitting

Fitting > Fitting module > About Fitting |

What is Fitting?

In the Fitting window, the selected model scenarios are run many times and the selected parameters to fit are changed many times in order to minimize the difference between data and model. When the fit can no longer be improved by adjusting the parameters, the Fitting module calculates a wide range of statistics to assess the quality of the fit (including maximum likelihood and confidence intervals on the parameters).

Automated fitting of a single set of parameters to multiple scenarios / experiments saves considerable time compared to classical and alternative methods (e.g. manual fit, or one experiment at a time, or one parameter at a time).

Typical fitted parameters

Mechanistic, predictive models are built by connecting rate processes together (such as reactions, heat transfer, mass transfer etc.) that may contain unknown **parameters** which govern their rate (in e.g. in mol/s or J/s). A parameter in this context is a variable used in the model which does not change during each simulation, but affects the predicted responses.

An example of reaction rate parameters are the reaction rate constants (e.g. at a reference temperature). Without realistic values for these, a kinetic model will not be useful. The most common fitted parameters are reaction kinetics, mass/heat transfer coefficients and filtration parameters.

Importance of experimental data

In order to estimate parameters some relevant **experimental data** will be required. Some model parameters can be directly measured (e.g. reaction heat from calorimetry), but it is often required to alter the unknown model parameters until the model results closely match the experimental data. The suitability of the data to fit the selected parameters is very important in getting good parameter estimates. Criteria for the closeness of the match ("goodness of fit") are required, which can include visual inspection of the data and model results and use of quantitative statistics, such as a sum of the squares of the differences between the data and the model. The Fitting module seeks to minimize a sum of squares (this is __weighted__ depending on the users selection).

What the fitting algorithm does

Fitting of parameters requires minimizing the difference between measured data and model results. A minimum can either be local (a minimum is found, but a better set of parameters exist) or global (the best possible set of parameters has been found). The Fitting module finds minima, but unfortunately there is no way to guarantee a global minimum. The easiest way to test for a local minimum is by restarting (repeating) a fit at the minimum, or by changing the initial guesses to see if the same parameter set is again obtained by fitting.

Required inputs for fitting

There are two main inputs required to run the Fitting module:

- Selection of data to fit (multiple data series over multiple scenarios can be used)
- Selection of model parameters to be fitted (reaction kinetics or scenarios sheet parameters can be selected)

The outputs of the module include:

- Fitted parameter values
- Confidence levels in the parameter values
- Analysis of the fit for each data series selected