rank_sampling

Sample allocation based on rank sampling within multilevel function train

Specification

• Alias: None

• Arguments: None

Description

Multilevel function train based on regression may allocate the number of samples per level based on the collocation ratio times the regression size. The regression size is determined by the rank per core and the basis order per dimension as described at function_train, where these ranks and orders may be either user-specified values (for initial sample allocation), incremented values (for external adaptation by Dakota), or recovered values (in the case of internal C3 adaptation using adapt_rank).

The adaptive algorithm starts from a pilot sample, shapes the profile based on the regression size computed from the current orders and recovered ranks, and iterates until convergence.

This capability is b experimental and under active development.

Examples

This example starts with rank-two order-two initial expansion for each level, with twice as many samples as regression coefficients. As the recovered rank is updated for each level, as dictated by the internal adapt_rank approach, the number of samples is incremented as needed in order to synchronize with the specified collocation ratio. In this case, the basis order is fixed and only the ranks and associated samples are updated for each level.

method,
 model_pointer = 'HIERARCH'
 multifidelity_function_train
   allocation_control rank_sampling
   p_refinement uniform
     start_rank_sequence  = 2 2 2 2 2
     adapt_rank  kick_rank = 2  max_rank  = 10
     start_order_sequence = 2 2 2 2 2
     collocation_ratio = 2.  seed = 160415
     convergence_tolerance = 1.e-2
     max_refinement_iterations = 5