Dakota Reference Manual  Version 6.4 Large-Scale Engineering Optimization and Uncertainty Analysis
rkd_darts

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

## Topics

This keyword is related to the topics:

## Specification

Alias: nond_rkd_darts

Argument(s): none

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 distribution Undocumented: Recursive k-d (RKD) Darts is an experimental capability.
Optional probability_levels Undocumented: Recursive k-d (RKD) Darts is an experimental capability.
Optional gen_reliability_levels Undocumented: Recursive k-d (RKD) Darts is an experimental capability.
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.