(Experimental) Adaptively select experimental designs for iterative Bayesian updating


  • Alias: None

  • Arguments: None

Child Keywords:


Description of Group

Dakota Keyword

Dakota Keyword Description



Number of data points used during initial Bayesian calibration



Number of candidate design points considered



Maximum number of high-fidelity model runs to be used



Number of optimal designs selected concurrently



Specify text file containing candidate design points



Use second Kraskov algorithm to compute mutual information


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 \(\xi_i\) in the set of possible design conditions, the mutual information (MI) between the low-fidelity model parameters \(\boldsymbol{\theta}\) and the high-fidelity model response \(\textbf{y}(\xi_i)\) ,

\[MI = \iint f(\boldsymbol{\theta}, \textbf{y}(\xi_i) ) \log \frac{ f(\boldsymbol{\theta}, \textbf{y}(\xi_i)) } { f(\boldsymbol{\theta}) f(\textbf{y}(\xi_i)) } d\boldsymbol{\theta} d\textbf{y},\]

is approximated. The high-fidelity model is replaced by the low-fidelity model and a \(k\) -nearest neighbor approximation is used in the calculation. The design point \(\xi^{*}\) for which MI is the largest is selected and run through the high-fidelity model to yield a new observation \(y(\xi^{*})\) . 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.