Dakota Reference Manual
Version 6.12
Explore and Predict with Confidence

Recursive kd (RKD) Darts: Recursive Hyperplane Sampling for Numerical Integration of HighDimensional Functions.
This keyword is related to the topics:
Alias: nond_rkd_darts
Argument(s): none
Child Keywords:
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required  build_samples  Number of initial model evaluations used in build phase  
Optional  seed  Seed of the random number generator  
Optional  lipschitz  Undocumented: Recursive kd (RKD) Darts is an experimental capability.  
Optional  samples_on_emulator  Number of samples at which to evaluate an emulator (surrogate)  
Optional  response_levels  Undocumented: Recursive kd (RKD) Darts is an experimental capability.  
Optional  probability_levels  Specify probability levels at which to estimate the corresponding response value  
Optional  gen_reliability_levels  Specify generalized relability levels at which to estimate the corresponding response value  
Optional  distribution  Selection of cumulative or complementary cumulative functions  
Optional  rng  Undocumented: Recursive kd (RKD) Darts is an experimental capability.  
Optional  model_pointer  Identifier for model block to be used by a method 
Disclaimer: The RKD method is currently in development mode, for further experimental verification. Please contact Dakota team if you have further questions about using this method.
Recursive kd (RKD) darts is an algorithm to evaluate the integration of a ddimensional black box function f(x) via recursive sampling over d, using a series of hyperplanes of variable dimensionality k = {d, d1, …, 0}. Fundamentally, we decompose the ddimensional integration problem into a series of nested onedimensional problems. That is, we start at the root level (the whole domain) and start sampling down using hyperplanes of one lower dimension, all the way down to zero (points). A ddimensional domain is subsampled using (d1) hyperplanes, a (d1)dimensional subdomain is subsampled using (d2) hyperplanes, and so on. Every hyperplane, regardless of its dimension, is evaluated using sampled hyperplanes of one lower dimension, as shown in the set of figures above. Each hyperplane has direct information exchange with its parent hyperplane of one higher dimension, and its children of one lower dimension.
In each onedimensional problem, we construct a piecewise approximation surrogate model, using 1dimensional Lagrange interpolation. Information is exchanged between different levels, including integration values, as well as interpolation and evaluation errors, in order to a) find the integration value up to that level, b) estimate the associated integration error, and c) guide the placement of future samples.