Organization of Results

Currently, complete or nearly complete coverage of results from sampling, optimization and calibration methods, parameter studies, and stochastic expansions exists. Coverage will continue to expand in future releases to include not only the results of all methods, but other potentially useful information such as interface evaluations and model tranformations.

Methods in Dakota have a character string Id and are executed by Dakota one or more times. (Methods are executed more than once in studies that include a nested model, for example.) The Id may be provided by the user in the input file using the id_method keyword, or it may be automatically generated by Dakota. Dakota uses the label NO_METHOD_ID for methods that are specified in the input file without an id_method, and NOSPEC_METHOD_ID_<N> for methods that it generates for its own internal use. The <N> in the latter case is an incrementing integer that begins at 1.

The results for the <N>th execution of a method that has the label <method Id> are stored in the group

/methods/<method Id>/results/execution:<N>/

The /methods group is always present in Dakota HDF5 files, provided at least one method added results to the output. (In a future Dakota release, the top level groups /interfaces and /models will be added.) The group execution:1 also is always present, even if there is only a single execution.

The groups and datasets for each type of result that Dakota is currently capable of storing are described in the following sections. Every dataset is documented in its own table. These tables include:

  • A brief description of the dataset.

  • The location of the dataset relative to /methods/<method Id>/execution:<N>. This path may include both literal text that is always present and replacement text. Replacement text is <enclosed in angle brackets and italicized>. Two examples of replacement text are <response descriptor> and <variable descriptor>, which indicate that the name of a Dakota response or variable makes up a portion of the path.

  • Clarifying notes, where appropriate.

  • The type (String, Integer, or Real) of the information in the dataset.

  • The shape of the dataset; that is, the number of dimensions and the size of each dimension.

  • A description of the dataset’s scales, which includes - The dimension of the dataset that the scale belongs to. - The type (String, Integer, or Real) of the information in the scale. - The label or name of the scale. - The contents of the scale. Contents that appear in plaintext are literal and will always be present in a scale. Italicized text describes content that varies. - notes that provide further clarification about the scale.

  • A description of the dataset’s attributes, which are key:value pairs that provide helpful context for the dataset.

The Expected Output section of each method’s keyword documentation indicates the kinds of output, if any, that method currently can write to HDF5. These are typically in the form of bulleted lists with clariying notes that refer back to the sections that follow.

Study Metadata

Several pieces of information about the Dakota study are stored as attributes of the top-level HDF5 root group (“/”). These include:

Label

Type

Description

dakota_version

String

Version of Dakota used to run the study

dakota_revision

String

Dakota version control information

output_version

String

Version of the output file

input

String

Dakota input file

top_method

String

Id of the top-level method

total_cpu_time

Real

Combined parent and child CPU time in seconds

parent_cpu_time

Real

Parent CPU time in seconds (when Dakota is built with UTILIB)

child_cpu_time

Real

Child CPU time in seconds (when Dakota is built with UTILIB)

total_wallclock_time

Real

Total wallclock time in seconds (when Dakota is built with UTILIB)

mpi_init_wallclock_time

Real

Wallclock time to MPI_Init in seconds (when Dakota is built with UTILIB and run in parallel)

run_wallclock_time

Real

Wallclock time since MPI_Init in seconds (when Dakota is built with UTILIB and run in parallel)

mpi_wallclock_time

Real

Wallclock time since MPI_Init in seconds (when Dakota is not built with UTILIB and run in parallel)

A Note about Variables Storage

Variables in most Dakota output (e.g. tabular data files) and input (e.g. imported data to construct surrogates) are listed in “input spec” order. (The variables keyword section is arranged by input spec order.) In this ordering, they are sorted first by function:

  1. Design

  2. Aleatory

  3. Epistemic

  4. State

And within each of these categories, they are sorted by domain:

  1. Continuous

  2. Discrete integer (sets and ranges)

  3. Discrete string

  4. Discrete real

A shortcoming of HDF5 is that datasets are homogeneous; for example, string- and real-valued data cannot readily be stored in the same dataset. As a result, Dakota has chosen to flip “input spec” order for HDF5 and sort first by domain, then by function when storing variable information. When applicable, there may be as many as four datasets to store variable information: one to store continuous variables, another to store discrete integer variables, and so on. Within each of these, variables will be ordered by function.

Sampling Moments

sampling produces moments (e.g. mean, standard deviation or variance) of all responses, as well as 95% lower and upper confidence intervals for the 1st and 2nd moments. These are stored as described below. When sampling is used in incremental mode by specifying refinement_samples, all results, including the moments group, are placed within groups named increment:<N>, where <N> indicates the increment number beginning with 1.

Moments

Description

1st through 4th moments for each response

Location

[increment:<N>]/moments/<response descriptor>

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

1-dimensional: length of 4

Type

Real

Scales

Dimension

Type

Label

Contents

Notes

0

String

moments

mean, std_deviation, skewness, kurtosis

Only for standard moments

0

String

moments

mean, variance, third_central, fourth_central

Only for central moments

Moment Confidence Intervals

Description

Lower and upper 95% confidence intervals on the 1st and 2nd moments

Location

moment_confidence_intervals/<response descriptor>

Shape

2-dimensional: 2x2

Type

Real

Scales

Dimension

Type

Label

Contents

Notes

0

String

bounds

lower, upper

1

String

moments

mean, std_deviation

Only for standard moments

1

String

moments

mean, variance

Only for central moments

Correlations

A few different methods produce information about the correlations between pairs of variables and responses (collectively: factors). The four tables in this section describe how correlation information is stored. One important note is that HDF5 has no special, native type for symmetric matrices, and so the simple correlations and simple rank correlations are stored in dense 2D datasets.

Simple Correlations

Description

Simple correlation matrix

Location

[increment:<N>]/simple_correlations

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

2-dimensional: number of factors by number of factors

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

Notes

0, 1

String

factors

Variable and response descriptors

false

The scales for both dimensions are identical

Simple Rank Correlations

Description

Simple rank correlation matrix

Location

[increment:<N>]/simple_rank_correlations

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

2-dimensional: number of factors by number of factors

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

Notes

0, 1

String

factors

Variable and response descriptors

false

The scales for both dimensions are identical

Partial Correlations

Description

Partial correlations

Location

[increment:<N>]/partial_correlations/<response descriptor>

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

1-dimensional: number of variables

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

variables

Variable descriptors

false

Partial Rank Correlations

Description

Partial Rank correlations

Location

[increment:<N>]/partial_rank_correlations/<response descriptor>

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

1-dimensional: number of variables

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

variables

Variable descriptors

false

Probability Density

Some aleatory UQ methods estimate the probability density of resposnes.

Probability Density

Description

Probability density of a response

Location

[increment:<N>]/probability_density/<response descriptor>

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

1-dimensional: number of bins in probability density

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

Real

lower_bounds

Lower bin edges

false

0

Real

upper_bounds

Upper bin edges

false

Level Mappings

Aleatory UQ methods can calculate level mappings (from user-specified probability, reliability, or generalized reliability to response, or vice versa).

Probability Levels

Description

Response levels corresponding to user-specified probability levels

Location

[increment:<N>]/probability_levels/<response descriptor>

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

1-dimensional: number of requested levels for the response

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

Real

probability_levels

User-specified probability levels

false

Reliability Levels

Description

Response levels corresponding to user-specified reliability levels

Location

[increment:<N>]/reliability_levels/<response descriptor>

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

1-dimensional: number of requested levels for the response

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

Real

reliability_levels

User-specified reliability levels

false

Generalized Reliability Levels

Description

Response levels corresponding to user-specified generalized reliability levels

Location

[increment:<N>]/gen_reliability_levels/<response descriptor>

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

1-dimensional: number of requested levels for the response

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

Real

gen_reliability_levels

User-specified generalized reliability levels

false

Response Levels

Description

Probability, reliability, or generalized reliability levels corresponding to user-specified response levels

Location

[increment:<N>]/response_levels/<response descriptor>

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

1-dimensional: number of requested levels for the response

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

Real

response_levels

User-specified response levels

false

Variance-Based Decomposition (Sobol’ Indices)

Dakota’s sampling method can produce main and total effects; stochastic expansions ( polynomial_chaos, stoch_collocation ) additionally can produce interaction effects.

Main Effects

Description

First-order Sobol’ indices

Location

main_effects/<response descriptor>

Shape

1-dimensional: number of variables

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

variables

Variable descriptors

false

Total Effects

Description

Total-effect Sobol’ indices

Location

total_effects/<response descriptor>

Shape

1-dimensional: number of variables

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

variables

Variable descriptors

false

Each order (pair, 3-way, 4-way, etc) of interaction is stored in a separate dataset. The scales are unusual in that they are two-dimensional to contain the labels of the variables that participate in each interaction.

Interaction Effects

Description

Sobol’ indices for interactions

Location

order_<N>_interactions/<response descriptor>

Shape

1-dimensional: number of Nth order interactions

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

Notes

0

String

variables

Descriptors of the variables in the interaction

false

Scales for interaction effects are 2D datasets with the dimensions (number of interactions, N)

Integration and Expansion Moments

Stochastic expansion methods can obtain moments two ways.

Integration Moments

Description

Moments obtained via integration

Location

integration_moments/<response descriptor>

Shape

4

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

Notes

0

String

moments

mean, std_deviation, skewness, kurtosis

Only for standard moments

0

String

moments

mean, variance, third_central, fourth_central

true

Only for central moments

Expansion Moments

Description

Moments obtained via expansion

Location

expansion_moments/<response descriptor>

Shape

4

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

Notes

0

String

moments

mean, std_deviation, skewness, kurtosis

Only for standard moments

0

String

moments

mean, variance, third_central, fourth_central

true

Only for central moments

Extreme Responses

sampling with epistemic variables produces extreme values (minimum and maximum) for each response.

Extreme Responses

Description

The sample minimum and maximum of each response

Location

[increment:<N>]/extreme_responses/<response descriptor>

Notes

The [increment:<N>] group is present only for sampling with refinement

Shape

2

Type

Real

Scales

Dimension

Type

Label

Contents

0

String

extremes

minimum, maximum

Parameter Sets

All parameter studies ( vector_parameter_study, list_parameter_study, multidim_parameter_study, centered_parameter_study ) record tables of evaluations (parameter-response pairs), similar to Dakota’s tabular output file. Centered parameter studies additionally store evaluations in an order that is more natural to intepret, which is described below.

In the tabular-like listing, variables are stored according to the scheme described in a previous section.

Parameter Sets

Description

Parameter study evaluations in a tabular-like listing

Location

parameter_sets/{continuous_variables, discrete_integer_variables, discrete_string_variables, discrete_real_variables, responses}

Shape

2-dimensional: number of evaluations by number of variables or responses

Type

Real, String, or Integer, as applicable

Scales

Dimension

Type

Label

Contents

Literal_contents

1

String

variables or responses

Variable or response descriptors

false

Variable Slices

Centered paramter studies store “slices” of the tabular data that make evaluating the effects of each variable on each response more convenient. The steps for each individual variable, including the initial or center point, and corresponding responses are stored in separate groups.

Variable Slices

Description

Steps, including center/initial point, for a single variable

Location

variable_slices/<variable descriptor>/steps

Shape

1-dimensional: number of user-specified steps for this variable

Type

Real, String, or Integer, as applicable

Variable Slices - Responses

Description

Responses for variable slices

Location

variable_slices/<variable descriptor>/responses

Shape

2-dimensional: number of evaluations by number of responses

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

1

String

responses

Response descriptors

false

Best Parameters

Dakota’s optimization and calibration methods report the parameters at the best point (or points, for multiple final solutions) discovered. These are stored using the scheme decribed in the variables section. When more than one solution is reported, the best parameters are nested in groups named set:<N>, where <N> is a integer numbering the set and beginning with 1.

State (and other inactive variables) are reported when using objective functions and for some calibration studies. However, when using configuration variables in a calibration, state variables are suppressed.

Best Parameters

Description

Best parameters discovered by optimization or calibration

Location

[set:<N>]/best_parameters/{continuous, discrete_integer, discrete_string, discrete_real}

Notes

The [set:<N>] group is present only when multiple final solutions are reported.

Shape

1-dimensional: number of variables

Type

Real, String, or Integer, as applicable

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

variables

Variable descriptors

false

Best Objective Functions

Dakota’s optimization methods report the objective functions at the best point (or points, for multiple final solutions) discovered. When more than one solution is reported, the best objective functions are nested in groups named set:<N>, where <N> is a integer numbering the set and beginning with 1.

Best Objective Functions

Description

Best objective functions discovered by optimization

Location

[set:<N>]/best_objective_functions

Notes

The [set:<N>] group is present only when multiple final solutions are reported.

Shape

1-dimensional: number of objective functions

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

responses

Response descriptors

false

Best Nonlinear Constraints

Dakota’s optimization and calibration methods report the nonlinear constraints at the best point (or points, for multiple final solutions) discovered. When more than one solution is reported, the best constraints are nested in groups named set:<N>, where N is a integer numbering the set and beginning with 1.

Best Nonlinear Constraints

Description

Best nonlinear constraints discovered by optimization or calibration

Location

[set:<N>]/best_constraints

Notes

The [set:<N>] group is present only when multiple final solutions are reported.

Shape

1-dimensional: number of nonlinear constraints

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

responses

Response descriptors

false

Calibration

When using calibration terms with an optimization method, or when using a nonlinear least squares method such as nl2sol, Dakota reports residuals and residual norms for the best point (or points, for multiple final solutions) discovered.

Best Residuals

Description

Best residuals discovered

Location

best_residuals

Shape

1-dimensional: number of residuals

Type

Real

Best Residual Norm

Description

Norm of best residuals discovered

Location

best_norm

Shape

Scalar

Type

Real

Parameter Confidence Intervals

Least squares methods (nl2sol, nlssol_sqp, optpp_g_newton) compute confidence intervals on the calibration parameters.

Parameter Confidence Intervals

Description

Lower and upper confidence intervals on calibrated parameters

Location

confidence_intervals

Notes

The confidence intervals are not stored when there is more than one experiment.

Shape

2-dimensional: 2x2

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

variables

Variable desriptors

false

1

String

bounds

lower, upper

Best Model Responses (without configuration variables)

When performing calibration with experimental data (but no configruation variables), Dakota records, in addition to the best residuals, the best original model resposnes.

Best Model Responses

Description

Original model responses for the best residuals discovered

Location

best_model_responses

Shape

1-dimensional: number of model responses

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

responses

Response descriptors

false

Best Model Responses (with configuration variables)

When performing calibration with experimental data that includes configuration variables, Dakota reports the best model responses for each experiment. These results include the configuration variables, stored in the scheme described in the variables section, and the model responses.

Best Configuration Variables for Experiment

Description

Configuration variables associated with experiment N

Location

best_model_responses/experiment:<N>/{continuous_config_variables, discrete_integer_config_variables, discrete_string_config_variables, discrete_real_config_variables}

Shape

1-dimensional: number of variables

Type

Real, String, or Integer, as applicable

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

variables

Variable descriptors

false

Best Model Responses for Experiment

Description

Original model responses for the best residuals discovered

Location

best_model_responses/experiment:<N>/responses

Shape

1-dimensional: number of model responses

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

String

responses

Response descriptors

false

Multistart and Pareto Set

The multi_start and pareto_set methods are meta-iterators that control multiple optimization sub-iterators. For both methods, Dakota stores the results of the sub-iterators (best parameters and best results). For multi_start, Dakota additionally stores the initial points, and for pareto_set, it stores the objective function weights.

Starting Points (multi_start)

Description

Starting points for multi_start

Location

starting_points/continuous

Notes

Currently only continuous starting points are supported by multi_start

Shape

2-dimensional: number of sets by number of variables

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

Integer

set_ids

set Ids

false

1

String

variables

Variable descriptors

false

Weights (pareto_set)

Description

Response Weights for pareto_set

Location

weights

Shape

2-dimensional: number of sets by number of responses

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

Integer

set_ids

set Ids

false

1

String

weights

w1, w2, … wN

true

Best Parameters (multi_start or pareto_set)

Description

Best parameters discovered by multi_start or pareto_set

Location

best_parameters/{continuous, discrete_integer, discrete_string, discrete_real}

Shape

2-dimensional: number of sets by number of variables

Type

Real, String, or Integer, as applicable

Scales

Dimension

Type

Label

Contents

Literal_contents

0

Integer

set_ids

set Ids

false

1

String

variables

Variable descriptors

false

Best responses

Description

Best responses for multi_start and pareto_set

Location

best_responses

Shape

2-dimensional: number of sets by number of responses

Type

Real

Scales

Dimension

Type

Label

Contents

Literal_contents

0

Integer

set_ids

set Ids

false

1

String

responses

Response descriptors

false