Dakota Reference Manual: experimental_design

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experimental_design

(Experimental) Adaptively select experimental designs for iterative Bayesian updating

## Specification

Alias: none

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Required | initial_samples | Number of data points used during initial Bayesian calibration
| Required | num_candidates | Number of candidate design points considered
| Optional | max_hifi_evaluations | Maximum number of high-fidelity model runs to be used
| Optional | batch_size | Number of optimal designs selected concurrently
| Optional | import_candidate_points_file | Specify text file containing candidate design points
| Optional | ksg2 | Use second Kraskov algorithm to compute mutual information

## Description

This "experimental design" algorithm uses responses produced by a high-fidelity model as data to update the parameters of a low-fidelity model using Bayes' Rule. It is a capability that is under active development and is currently compatible only with `queso`. The user-specified high-fidelity model should depend only on configuration variables (i.e. design conditions), such as temperature or spatial location, while the user-specified low-fidelity model should depend on both configuration variables and its own model parameters to be calibrated.

The algorithm starts with a preliminary Bayesian calibration using the number of data points specified in `initial_samples`. These data points can be read in through the `calibration_data_file` command in the `responses` block. If `num_experiments` is less than `initial_samples` or if no such data file is provided, Latin Hypercube Samples of the design space (specified in the `variables` block) will be run through the user-specified high-fidelity code to supplement the initial data. Once this first calibration is complete, a set of possible experimental design conditions, specified using the configuration variables, is proposed. The user specifies the size of this set using `num_candidates`. The set of candidates itself may be explicitly given through the `import_candidate_points_file` command. If the number of candidates in this file is less than `num_candidates`, or if this file is omitted, the set of candidate designs will again be supplemented with a Latin Hypercube Sample of the design space.

For each candidate design in the set of possible design conditions, the mutual information (MI) between the low-fidelity model parameters and the high-fidelity model response ,

is approximated. The high-fidelity model is replaced by the low-fidelity model and a -nearest neighbor approximation is used in the calculation. The design point for which MI is the largest is selected and run through the high-fidelity model to yield a new observation . This new observation is added to the calibration data, and a subsequent Bayesian calibration is performed. A new MI for each remaining candidate design is computed, and the process repeats until one of three stopping criteria are met. Multiple optimal designs may be selected concurrently by specifying `batch_size`.

Of the three stopping criteria, two are automatically checked by Dakota. If the relative change in the MI from one iteration to the next is sufficiently small or if the set of candidate design conditions has been exhausted, the algorithm teriminates. The user may specify the third stopping criteria using `max_hifi_evaluations`. This limits the number of high-fidelity model evaluations that will be performed during this algorithm. It therefore limits the number of iterations through the algorithm that will be performed. Any high-fidelity model runs needed to produce the data set for the initial calibration are not included in this allocation.

In the case that the high-fidelity model must be run indepently of Dakota, the user may set `max_hifi_evaluations` to zero. The optimal experimental design point will be calculated and reported, but the high-fidelity model will not be run. For more details, see the User's Manual.

Expected Output

Information regarding the progress and termination condition of the experimental design algorithm is output to the screen with varying levels of verbosity. Further details can be found, regardless of verbosity, in the output file `experimental_design_output.txt`

Usage Tips

Due to the optional file read-ins and the supplemental sampling, it is important for the user to check consistency within the input file specifications. For example, if `num_experiments` is less than the number of experiments in the `calibration_data_file`, only the first lines of the file will be used and the rest will be discarded. The same holds true for the `import_candidate_points_file` and `num_candidates`.

## Examples

The input file below illustrates the use of `experimental_design` and its options

        bayes_calibration
          queso
          dram
          chain_samples = 1000 seed = 348
        experimental_design
          initial_samples = 5
          num_candidates = 10
          import_candidate_points_file = "bayes_experimental_design.cand.dat"
            freeform
          max_hifi_evaluations = 3