Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2016018697
pages 1-21

VPS: VORONOI PIECEWISE SURROGATE MODELS FOR HIGH-DIMENSIONAL DATA FITTING

Ahmad A. Rushdi
Department of Electrical and Computer Engineering, University of California, Davis, California 95616, USA; Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
Laura P. Swiler
Optimization and Uncertainty Quantification Department, Sandia National Laboratories, P.O. Box 5800, MS 1318, Albuquerque, New Mexico 87185, USA
Eric T. Phipps
Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
Marta D'Elia
Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
Mohamed S. Ebeida
Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA

ABSTRACT

Surrogate models (metamodels) are indispensable for numerical simulations over high-dimensional spaces. They typically use well-selected samples of the expensive code runs to produce a cheap-to-evaluate model. We introduce a new method to construct credible global surrogates with local accuracy without dictating where to sample: Voronoi piecewise surrogate (VPS) models. The key component in our method is to implicitly decompose the parameter space into cells using the Voronoi tessellation around the sample points as seeds, via an approximate dual Delaunay graph. While explicit domain decompositions have storage and processing requirements that exponentially grow with dimension, VPS construction counts on the implicitness of Voronoi cells and the one-to-one mapping between seeds and cells, regardless of dimension, to avoid this curse of dimensionality. Each implicit cell can then use information provided by its neighbors to build its own local piece of the global surrogate. The piecewise locality breaks down the high-order approximation problem into a set of low-order problems, with better immunity against numerical oscillations. Domain points can be assigned to cells using a simple nearest seed search. Furthermore, a VPS model is naturally updated with the addition of new samples, can handle smooth and discontinuous functions, and can adopt a parallel implementation. We demonstrate the application of VPS models to numerical integration and probability of failure estimation problems.