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:
Design
Aleatory
Epistemic
State
And within each of these categories, they are sorted by domain:
Continuous
Discrete integer (sets and ranges)
Discrete string
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
Total Effects |
|||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Description |
Total-effect Sobol’ indices |
||||||||||
Location |
total_effects/<response descriptor> |
||||||||||
Shape |
1-dimensional: number of variables |
||||||||||
Type |
Real |
||||||||||
Scales |
|
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 |
|
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 |
|
Expansion Moments |
|||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Description |
Moments obtained via expansion |
||||||||||||||||||
Location |
expansion_moments/<response descriptor> |
||||||||||||||||||
Shape |
4 |
||||||||||||||||||
Type |
Real |
||||||||||||||||||
Scales |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
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 |
|
Weights (pareto_set) |
||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Description |
Response Weights for pareto_set |
|||||||||||||||
Location |
weights |
|||||||||||||||
Shape |
2-dimensional: number of sets by number of responses |
|||||||||||||||
Type |
Real |
|||||||||||||||
Scales |
|
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 |
|
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 |
|