greedy

Sample allocation based on greedy refinement within multifidelity function train

Specification

• Alias: None

• Arguments: None

Description

Multifidelity function train supports greedy refinement strategies based on regression approaches for computing expansion coefficients. The key idea is that each level of the model hierarchy being approximated can generate one or more candidates for refinement. These candidates are competed against each other within a unified competition, and the candidate that induces the largest change in the statistical QoI (response covariance by default, or results of any $z/p/\beta /{\beta }^{\ast }$ level mappings when specified), normalized by relative cost of evaluating the candidate, is selected and then used to generate additional candidates for consideration at its model level.

Examples

The following example of greedy multifidelity function train starts from a rank-two order-two reference expansion for each level, with twice as many samples as regression coefficients, and generates candidate refinements for each level that are competed in an integrated greedy competition. The number of new samples for the incremented candidate is determined from the collocation ratio times the regression size (which may either be fixed or adapted in the case of adapt_rank). In this example, the number of candidates for each level is limited to one uniform refinement of the current expansion, and uniform refinement currently involves an advancement in the basis order for all approximation cores in combination with a rank adaptation between two and ten, incrementing in steps of two.

method,
 model_pointer = 'HIERARCH'
 multifidelity_function_train
   allocation_control greedy
   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  max_order = 10
     collocation_ratio = 2.  seed = 160415
     convergence_tolerance = 1.e-2
     max_refinement_iterations = 5