The Curve Fitting Study
The Curve Fitting () study node provides a simplified interface for performing least-squares parameter estimation. It can be used when the reference data is a function of time or a single parameter, and the multiphysics model result expected to match the data is a single global expression evaluated for a selected study step in the same study.
When the reference data consists of measured values, you typically first import it as an interpolation function which you can easily plot and visually compare to the result of your multiphysics model. The Curve Fitting study node can refer directly to the interpolation function and is independent of whether the interpolation function was specified directly in the user interface or imported from a file, and is also independent of the file format used.
Alternately, the reference data can be given as a user-defined expression which is evaluated at the time steps or parameter values specified in the corresponding study step. This is useful, for example, when estimating coefficients of a polynomial expected to match the model output, and in general when estimating parameters in a mathematical model intended to replicate the output of the full multiphysics model.
The parameter estimation problem is implemented as an optimization problem minimizing a sum of squared differences between model and reference data. The sum is computed over time or parameter steps as specified either in the argument column of an interpolation function used as reference data, or in the study step selected for evaluation of the model data.
Model Data
Choose one of the allowed study steps from the Study step list. Only time dependent study steps are supported. Click the Go to Source button ) to move to the Settings window for the selected study node. Enter a global Model expression, which is evaluated at each time or parameter step where it is compared to the corresponding reference data. You can also click the Add Expression () and Replace Expression () buttons to search through a list of predefined expressions.
Reference Data
Select a Reference data source: Interpolation function or User defined. If you choose an interpolation function as data source, its argument column will decide at which time or parameter values the difference between model and reference data is evaluated. When the data source is set to User defined, enter a Reference expression or click the Replace Expression () buttons to search through a list of predefined expressions. You can also press Ctrl+Space to add a predefined expression to the text field. The difference between the Model expression and the Reference expression is then evaluated at output time steps or parameter values as specified in the selected Study step.
Parameters
The settings in the Parameters section are identical to the corresponding settings in the Parameter Estimation study step. See Estimated Parameters under The Parameter Estimation Study.
Parameter Estimation Method
The settings in the Parameter Estimation Method section are identical to the corresponding settings in the Parameter Estimation study step. See Parameter Estimation Method under The Parameter Estimation Study.
Output While Solving
The settings in the Output While Solving section are identical to the corresponding settings in the Optimization study step. See Output While Solving under The Optimization Study.