1Blurb:: Sample allocation based on greedy refinement within multifidelity stochastic collocation 2 3Description:: 4 5Multifidelity stochastic collocation supports greedy refinement 6strategies using tensor and sparse grids for both nodal and 7hierarchical collocation approaches. The key idea is that each level 8of the model hierarchy being approximated can generate one or more 9candidates for refinement. These candidates are competed against each 10other within an integrated competition, and the candidate that induces the 11largest change in the statistical QoI (response covariance by default, 12or results of any level mappings when specified), normalized by 13relative cost of evaluating the candidate, is selected and then used 14to generate additional candidates for consideration at its model level. 15 16Topics:: 17 18Examples:: 19 20The following example of greedy multifidelity stochastic collocation 21using nodel interpolation starts from a zeroth-order expansion (a 22constant) for each level, and generates uniform candidate refinements 23for each level that are competed in a greedy competition. The number 24of new samples for the incremented candidate expansion order is 25determined from the quadrature rules of the new sparse grid level. In 26this case, the number of candidates for each level is limited to one 27uniform refinement of the current sparse grid level. 28 29\verbatim 30method, 31 model_pointer = 'HIERARCH' 32 multifidelity_stoch_collocation 33 nodal 34 allocation_control greedy 35 p_refinement uniform 36 sparse_grid_level_sequence = 0 unrestricted 37 convergence_tolerance 1.e-3 38\endverbatim 39 40The next example employs generalized sparse grids and hierarchical 41interpolation. Each level starts from a level 0 reference grid (a 42single point) and generates multiple admissible index set candidates. 43The full set of candidates across all levels is competed within a 44unified greedy competition, where the greedy selection metric is the 45induced change in the statistical QoI, normalized by the aggregate 46simulation cost of the index set candidate. In this case, there are 47multiple candidates for each level and the number of candidates grows 48rapidly with random dimension and grid level. 49 50\verbatim 51method, 52 model_pointer = 'HIERARCH' 53 multifidelity_stoch_collocation 54 hierarchical 55 allocation_control greedy 56 p_refinement dimension_adaptive generalized 57 sparse_grid_level_sequence = 0 unrestricted 58 convergence_tolerance 1.e-8 59\endverbatim 60 61Theory:: 62 63Faq:: 64See_Also:: 65