Dakota Reference Manual: responses

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responses

Description of the model output data returned to Dakota upon evaluation of an interface.

## Topics

This keyword is related to the topics:

- block

## Specification

Alias: none

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Optional | id_responses | Name the responses block; helpful when there are multiple
| Optional | descriptors | Labels for the responses
| Required (Choose One) | Response Type (Group 1) | objective_functions | Response type suitable for optimization
calibration_terms | Response type suitable for calibration or least squares
response_functions | Generic response type
| Required (Choose One) | Gradient Type (Group 2) | no_gradients | Gradients will not be used
analytic_gradients | Analysis driver will return gradients
mixed_gradients | Gradients are needed and will be obtained from a mix of numerical and analytic sources
numerical_gradients | Gradients are needed and will be approximated by finite differences
| Required (Choose One) | Hessian Type (Group 3) | no_hessians | Hessians will not be used
numerical_hessians | Hessians are needed and will be approximated by finite differences
quasi_hessians | Hessians are needed and will be approximated by secant updates (BFGS or SR1) from a series of gradient evaluations
analytic_hessians | Hessians are needed and are available directly from the analysis driver
mixed_hessians | Hessians are needed and will be obtained from a mix of numerical, analytic, and "quasi" sources

## Description

The `responses` specification in a Dakota input file indicates the types of data that can be returned by an interface when invoked during Dakota's execution. The specification includes three groups and two optional keywords.

The response type groupindicates the type and number of responses expected by Dakota. It must be one of three types:

1. Optimization: objective and constraint functions
2. Calibration: calibration (least squares) terms and constraint functions
3. Uncertainty Quantifiation: generic response functions

The response type specified should be consistent with the iterative technique called for in the method specification. Certain general-purpose iterative techniques, such as parameter studies and design of experiments methods, can be used with any of these response types.

The gradient type group indicates the availability of first derivatives (gradient vectors) for the response functions.

The gradient specification also links back to the iterative method used. Gradients commonly are needed when the iterative study involves gradient-based optimization, local reliability analysis for uncertainty quantification, or local sensitivity analysis. They can optionally be used to build some types of surrogate models.

The Hessian type group specifies the availability of second derivatives (Hessian matrices) for the response functions.

Hessian availability for the response functions is similar to the gradient availability specifications, with the addition of support for "quasi-Hessians". The Hessian specification also links back to the iterative method in use; Hessians commonly would be used in gradient-based optimization by full Newton methods or in reliability analysis with second-order limit state approximations or second-order probability integrations.

## Examples

Several examples follow. The first example shows an optimization data set containing an objective function and two nonlinear inequality constraints. These three functions have analytic gradient availability and no Hessian availability.

    responses
      objective_functions = 1
        nonlinear_inequality_constraints = 2
      analytic_gradients
      no_hessians

The next example shows a typical specification for a calibration data set. The six residual functions will have numerical gradients computed using the dakota finite differencing routine with central differences of 0.1% (plus/minus delta relative to current variables value = .001*value).

    responses
      calibration_terms = 6
      numerical_gradients
        method_source dakota
        interval_type central
        fd_gradient_step_size = .001
      no_hessians

The last example shows a generic specification that could be used with a nondeterministic sampling iterator. The three response functions have no gradient or Hessian availability; therefore, only function values will be used by the iterator.

    responses
      response_functions = 3
      no_gradients
      no_hessians

Parameter study and design of experiments iterators are not restricted in terms of the response data sets which may be catalogued; they may be used with any of the function specification examples shown above.

## Theory

Responses specify the total data set that is available for use by the method over the course of iteration. This is distinguished from the data subset described by an active set vector (see Dakota File Data Formats in the Users Manual [Adams et al., 2010]) indicating the particular subset of the response data needed for a particular function evaluation. Thus, the responses specification is a broad description of the data to be used during a study whereas the active set vector indicates the subset currently needed.