Dakota Reference Manual
Version 6.16
Explore and Predict with Confidence

Response type suitable for calibration or least squares
Alias: least_squares_terms num_least_squares_terms
Argument(s): INTEGER
Child Keywords:
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_scales  Characteristic values to scale each calibration term  
Optional  weights  Specify weights for each objective function  
Optional (Choose One)  Calibration Data (Group 1)  calibration_data  Supply field or mixed field/scalar calibration data  
calibration_data_file  Supply scalar calibration data only  
Optional  simulation_variance  Variance applied to simulation 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:
Note that the problem specification affects what must be returned to Dakota in the results_file :
Constraints
(See general problem formulation at objective_functions.) The keywords nonlinear_inequality_constraints and nonlinear_equality_constraints specify the number of nonlinear inequality constraints g, and nonlinear equality constraints h, respectively. When interfacing to external applications, the responses must be returned to Dakota in this order in the results_file :
An optimization problem's linear constraints are provided to the solver at startup only and do not need to be included in the data returned on every function evaluation. Linear constraints are therefore specified in the variables block through the linear_inequality_constraint_matrix and linear_equality_constraint_matrix .
Lower and upper bounds on the design variables x are also specified in the variables block.
Problem Transformations
Weighting or scaling calibration terms is often appropriate to account for measurement error or to condition the problem for easier solution. Weighting or scaling transformations are applied in the following order:
When present, observation error variance or full covariance , optionally specified through experiment_variance_type
, is applied to residuals first:
resulting in the typical varianceweighted least squares formulation
Any active scaling transformations are applied next, e.g., for characteristic value scaling:
Finally the optional weights are applied in a way that preserves backward compatibility:
so the ultimate least squares formulation, e.g., in a scaled and weighted case would be
Note that specifying observation error variance and weights are mutually exclusive in a calibration problem.
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: