ensemble
Ensemble surrogates employ a collection of lowerfidelity models to approximate a truth reference model at reduced cost.
Specification
Alias: None
Arguments: None
Child Keywords:
Required/Optional 
Description of Group 
Dakota Keyword 
Dakota Keyword Description 

Required (Choose One) 
Ensemble model specification 
Specification of an hierarchy of model fidelities, ordered from low to high. 

Pointer to specify a “truth” model, from which to construct a surrogate 
Description
Multifidelity modeling involves the use of lowerfidelity physicsbased models as surrogates for a highfidelity “truth” model. These lowfidelity models can involve variations in model form, resolution, or both. Model form variations for reduced fidelity may involve omitted physics or solution of approximated or averaged physics. Resolution variations typically involve coarsened spacetime discretizations (e.g., h derefinement), reduced element order (e.g., p derefinement), or loosened convergence tolerances. Unlike local, global, and multipoint surrogates, these approximations are not datadriven (no highfidelity data required for construction) and are standalone simulation models in their own right. As an example from computational fluid dynamics (CFD), both model form and resolution are varied when an inviscid, incompressible Euler model on a coarse discretization is used as a lowfidelity surrogate for a highfidelity large eddy simulation (LES) model on a fine discretization.
There are two specification options for identifying the ensemble of
models. First, the ordered_model_fidelities
specification points
to a sequence of model specifications of varying fidelity, ordered
from lowest to highest fidelity. The highest fidelity model in this
list provides the “truth” model, and each of the lower fidelity
alternatives provides different levels of approximation at different
levels of cost. This specification defines the sequence of all model
forms, where each model specification identified in this ordered
listing can additionally identify a set of resolution controls.
Either or both of these sequences may be specified, and this is
referred to as a “multilevel hierarchy” in the case of a hierarchy of
resolutions (one entry in ordered_model_fidelities
that includes
active resolution control), a “multifidelity hierarchy” in the case of
a hierarchy of model forms (multiple entries in
ordered_model_fidelities
without active resolution control), or a
“multilevelmultifidelity hierarchy” in the case of twodimensional
hierarchy including both model forms and resolutions (multiple entries
in ordered_model_fidelities
with one or more including active
resolution control). Note that the multilevelmultifidelity case can
be “ragged” in the sense that not all models need to provide the same
number of (or any) resolution controls.
Second, an unordered or “nonhierarchical” ensemble of models may be
specified using truth_model_pointer
in combination with
approximation_models
, where the latter defines the set of
unordered approximations to the highfidelity reference model. Note
that the distinction between ordered and unordered approximations is
of little consequence within the ensemble surrogate model
implementation; rather it becomes important when aligning with the
requirements of multifidelity algorithms that either assume ordered
hierarchies or provide the flexibility to leverage general
approximation ensembles.
The correction
specification identifies what type ( additive
,
multiplicative
, combined
) and order ( zeroth_order
,
first_order
, second_order
) of correction technique will be applied
to the low fidelity results in order to match high fidelity results
(value and potentially gradient and Hessian) at one or more points. As
described below, this is essential in the optimization context.
Use cases
In multifidelity surrogatebased optimization (SBO), the search
algorithm relies primarily on the lower fidelity models, which are
corrected for consistency with higher fidelity models. The higher
fidelity models are used primarily for verifying candidate steps based
on solution of low fidelity approximate subproblems and for updating
low fidelity corrections. In the hierarchical SBO case (as compared
to SBO with data fits), the correction
specification is required,
since the omission of a correction technique would effectively
eliminate the purpose of the high fidelity model (to use a low
fidelity model without corrections, then a single
model can be used
rather than a hierarchical
model). Refer to
global
for additional information on available
correction approaches.
In multifidelity uncertainty quantification (UQ), response differences are tracked for purposes of decomposing variance across model/resolution levels or for constructing separate discrepancy emulators. In this context, correction specifications are still valid for defining discrepancy emulation details but they are optional with the most common cases used as defaults.
Examples
Theory: