rkd_darts

Recursive k-d (RKD) Darts: Recursive Hyperplane Sampling for Numerical Integration of High-Dimensional Functions.

Specification

  • Alias: nond_rkd_darts

  • Arguments: 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 k-d (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 k-d (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 k-d (RKD) Darts is an experimental capability.

Optional

model_pointer

Identifier for model block to be used by a method

Description

* 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 k-d (RKD) darts is an algorithm to evaluate the integration of a d-dimensional black box function f(x) via recursive sampling over d, using a series of hyperplanes of variable dimensionality k = {d, d-1, …, 0}. Fundamentally, we decompose the d-dimensional integration problem into a series of nested one-dimensional 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 d-dimensional domain is subsampled using (d-1) hyperplanes, a (d-1)-dimensional sub-domain is subsampled using (d-2) 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 one-dimensional problem, we construct a piecewise approximation surrogate model, using 1-dimensional 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. Topics:: uncertainty_quantification