greedy

Sample allocation based on greedy refinement within multifidelity polynomial chaos

Specification

• Alias: None

• Arguments: None

Description

Multifidelity polynomial chaos supports greedy refinement strategies, spanning regression and projection 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 \(z/p/\beta/\beta^*\) 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 regression starts from a zeroth-order reference expansion (a constant) for each level, and generates candidate refinements for each level that are competed in an integrated greedy competition. The number of new samples for the incremented candidate expansion order is determined from the collocation ratio. In this case, the number of candidates for each level is limited to one uniform refinement of the current expansion order.

method,
 model_pointer = 'HIERARCH'
 multifidelity_polynomial_chaos
   allocation_control greedy
   p_refinement uniform
     expansion_order_sequence = 0
     collocation_ratio = .9  seed = 160415
     orthogonal_matching_pursuit
     convergence_tolerance 1.e-2

The next example employs generalized sparse grids within a greedy multifidelity competition. Each modeling level starts from a level 0 reference grid (a single point) and generates multiple admissible index set candidates. The full set of candidates across all model levels is competed within an integrated greedy competition, where the greedy selection metric is the induced change in the statistical QoI, normalized by the aggregate simulation cost of the index set candidate. In this case, there are multiple candidates for each model level and the number of candidates grows rapidly with random dimension and grid level.

method,
 model_pointer = 'HIERARCH'
 multifidelity_polynomial_chaos
   allocation_control greedy
   p_refinement dimension_adaptive generalized
     sparse_grid_level_sequence = 0 unrestricted
     convergence_tolerance 1.e-8