weighted
Include control variate weights for each of the recursive differences using in multilevel Monte Carlo (MLMC)
Specification
Alias: None
Arguments: None
Child Keywords:
Required/Optional |
Description of Group |
Dakota Keyword |
Dakota Keyword Description |
|---|---|---|---|
Optional |
For weighted multilevel Monte Carlo, this option activates a search over possible hierarchical model graphs |
||
Description
Referring to generalized ACV (search_model_graphs and [BLWL22]),
weighted MLMC is a special case of generalized ACV-RD (acv_recursive_diff) where a hierarchical DAG is
employed across the model approximations. As such, a weighted MLMC
specification forwards to the generalized ACV solver, but with fixing
the DAG to be hierarchical (each approximation node points to the next
approximation of higher fidelity/resolution, ending with the truth model
at the root node) and fixing the sampling scheme to be ACV-RD.
While the use of a hierarchical DAG is required, the approximation
selections and orderings within this DAG can be varied, so generalized
ACV capabilities for model graph search (different hierarchical
orderings) and model selection (different approximation subsets) are
available for a specification of weighted MLMC – see
search_model_graphs.
Theory
Refer to [BLWL22] for understanding ACV generalizations for the different control variate pairings that are possible when codified into a more comprehensive set of potential DAGs.
