Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Response type suitable for calibration or least squares
Alias: least_squares_terms num_least_squares_terms
Argument(s): INTEGER
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  scalar_calibration_terms  Number of scalar calibration terms  
Optional  field_calibration_terms  Number of field calibration terms  
Optional  primary_scale_types  Choose a scaling type for each response  
Optional  primary_scales  Supply a characteristic value to scale each reponse  
Optional  weights  Apply different weights to each response  
Optional (Choose One)  Group 1  calibration_data  Supply calibration data in the case of field data or mixed data (both scalar and field data).  
calibration_data_file  Specify a text file containing calibration data for scalar responses  
Optional  nonlinear_inequality_constraints  Group to specify nonlinear inequality constraints  
Optional  nonlinear_equality_constraints  Group to specify nonlinear equality constraints 
Responses for a calibration study are specified using calibration_terms
and optional keywords for weighting/scaling, data, and constraints. In general when calibrating, Dakota automatically tunes parameters to minimize discrepancies or residuals between the model and the data:
There are two use cases:
Constraints
The keywords nonlinear_inequality_constraints
, and nonlinear_equality_constraints
specify the number of nonlinear inequality constraints, and nonlinear equality constraints, respectively. When interfacing to external applications, the responses must be returned to Dakota in this order: calibration terms, nonlinear_inequality_constraints, then nonlinear_equality_constraints.
Any linear constraints present in an application need only be input to an optimizer at start up and do not need to be part of the data returned on every function evaluation. These are therefore specified in the method block.
Optional Keywords
The optional keywords relate to scaling responses (for better numerical results), dealing with multiple residuals, and importing data.
See the scaling
keyword in the method section for more details on scaling. If scaling is specified, then it is applied to each residual prior to squaring:
In the case where experimental data uncertainties are supplied, then the weights are automatically defined to be the inverse of the experimental variance:
Dakota calibration terms are typically used to solve problems of parameter estimation, system identification, and model calibration/inversion. Local least squares calibration problems are most efficiently solved using specialpurpose least squares solvers such as GaussNewton or LevenbergMarquardt; however, they may also be solved using any generalpurpose optimization algorithm in Dakota. While Dakota can solve these problems with either least squares or optimization algorithms, the response data sets to be returned from the simulator are different when using objective_functions versus calibration_terms.
Least squares calibration involves a set of residual functions, whereas optimization involves a single objective function (sum of the squares of the residuals), i.e.,
where f is the objective function and the set of are the residual functions, most commonly defined as the difference between a model response and data. Therefore, function values and derivative data in the least squares case involve the values and derivatives of the residual functions, whereas the optimization case involves values and derivatives of the sum of squares objective function. This means that in the least squares calibration case, the user must return each of n
residuals separately as a separate calibration term. Switching between the two approaches sometimes requires different simulation interfaces capable of returning the different granularity of response data required, although Dakota supports automatic recasting of residuals into a sum of squares for presentation to an optimization method. Typically, the user must compute the difference between the model results and the observations when computing the residuals. However, the user has the option of specifying the observational data (e.g. from physical experiments or other sources) in a file.
These keywords may also be of interest: