approximate_control_variate
Approximate control variate (ACV) sampling methods for UQ
Specification
Alias: acv_sampling
Arguments: None
Child Keywords:
Required/Optional 
Description of Group 
Dakota Keyword 
Dakota Keyword Description 

Required (Choose One) 
Solution Approach 
Approximate control variate (ACV) algorithm that employs independent samples per model 

Approximate control variate (ACV) algorithm that mimics MFMC by employing a nested pyramid sample pattern This ACV variant uses sample set definitions that are similar to multifidelity Monte Carlo (MFMC), in that sample sets are nested with each new level adding an increment on top of the previous. 

Weighted recursive difference option for approximate control variate sampling (ACVRD) 

Optional 
Perform a recursion of admissible DAGs for a given model ensemble 

Optional 
Initial set of samples for multilevel/multifidelity sampling methods. 

Optional 
Solution mode for multilevel/multifidelity methods 

Optional 
Option to suppress any increment to the number of truth samples 

Optional (Choose One) 
Optimization Solver 
Uses a sequential quadratic programming method for underlying optimization 

Uses a nonlinear interior point method for underlying optimization 

Optional 
Sequence of seed values for multistage random sampling 

Optional 
Reuses the same seed value for multiple random sampling sets 

Optional 
Selection of sampling strategy 

Optional 
Enable export of multilevel/multifidelity sample sequences to individual files 

Optional 
Stopping criterion based on relative error reduction 

Optional 
Number of iterations allowed for optimizers and adaptive UQ methods 

Optional 
Stopping criterion based on maximum function evaluations 

Optional 
Indicate the type of final statistics to be returned by a UQ method 

Optional 
Selection of a random number generator 

Optional 
Identifier for model block to be used by a method 
Description
An adaptive sampling method that utilizes multifidelity relationships in order to improve efficiency through variance reduction. It employs an ensemble model to manage an unordered set of lowerfidelity approximations to a single truth model.
Compared to multifidelity Monte Carlo (MFMC), ACV relaxes the nested sampling of a recursive emulator, instead targeting the truth model’s variance with each control variate pair. While the ensemble of control variates appears identical to MFMC:
the sample patterns used for the constituent estimators differ as depicted in Gorodetsky et al. (2020), Figure 2. Two ACV variants are currently implemented, ACVMF and ACVIS, with ACVKL to follow.
Default Behavior
The approximate_control_variate
method employs Monte Carlo sample
sets by default, but this default can be overridden to use Latin
hypercube sample sets using sample_type
lhs
.
Expected Output
The approximate_control_variate
method reports estimates of the
first four moments and a summary of the evaluations performed for each
model fidelity and discretization level. The method does not support
any level mappings (response, probability, reliability, generalized
reliability) at this time.
Expected HDF5 Output
If Dakota was built with HDF5 support and run with the
hdf5
keyword, this method
writes the following results to HDF5:
Sampling Moments (moments only, not confidence intervals)
In addition, the execution group has the attribute equiv_hf_evals
, which
records the equivalent number of highfidelity evaluations.
Usage Tips
The approximate_control_variate
method must be used in combination
with an ensemble model specification that defines either a
model form sequence or a discretization level sequence. For a model
form sequence, each model must provide a scalar
solution_level_cost
. For a discretization level sequence,
solution_level_control
must identify the variable string descriptor
that controls the resolution levels and the associated array of
relative costs must be provided using solution_level_cost
.
Examples
The following method block:
method,
model_pointer = 'NONHIER'
approximate_control_variate
acv_mf nip
pilot_samples = 20 seed = 1237
max_iterations = 10
convergence_tolerance = .001
specifies ACVMF using the nonlinear interior point (NIP) solver in combination with the model identified by the NONHIER pointer.
This NONHIER model specification provides a onedimensional sequence, here defined by a single truth model and a set of unordered approximation models, each with a single (or default) discretization level:
model,
id_model = 'NONHIER'
surrogate ensemble
truth_model = 'HF'
unordered_model_fidelities = 'LF1' 'LF2'
model,
id_model = 'LF1'
interface_pointer = 'LF1_INT'
simulation
solution_level_cost = 1
model,
id_model = 'LF2'
interface_pointer = 'LF2_INT'
simulation
solution_level_cost = 16
model,
id_model = 'HF'
interface_pointer = 'HF_INT'
simulation
solution_level_cost = 256.
Refer to dakota/test/dakota_uq_diffusion_acv3_cost4
.in and
dakota/test/dakota_uq_tunable_acv
.in in the source distribution
for this case as well as additional examples.
Refer to [Gorodetsky et al., JCP (408), 2020] for more detailed algorithm descriptions, theoretical considerations, and a helpful sample set diagram.