年間 6 号発行
ISSN 印刷: 2152-5080
ISSN オンライン: 2152-5099
Indexed in
VPS: VORONOI PIECEWISE SURROGATE MODELS FOR HIGH-DIMENSIONAL DATA FITTING
要約
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.
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