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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.2012003955
pages 119-141

ADAPTIVE SAMPLING WITH TOPOLOGICAL SCORES

Dan Maljovec
Scientific Computing and Imaging Institute, University of Utah, 72 South Central Campus Drive, Salt Lake City, Utah 84112, USA
Bei Wang
Scientific Computing and Imaging Institute, University of Utah, 72 South Central Campus Drive, Salt Lake City, Utah 84112, USA
Ana Kupresanin
Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 945509234, USA
Gardar Johannesson
Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 945509234, USA
Valerio Pascucci
Scientific Computing and Imaging Institute, University of Utah, 72 South Central Campus Drive, Salt Lake City, Utah 84112, USA
Peer-Timo Bremer
Scientific Computing and Imaging Institute, University of Utah, 72 South Central Campus Drive, Salt Lake City, Utah 84112, USA; Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 945509234, USA

ABSTRACT

Understanding and describing expensive black box functions such as physical simulations is a common problem in many application areas. One example is the recent interest in uncertainty quantification with the goal of discovering the relationship between a potentially large number of input parameters and the output of a simulation. Typically, the simulation of interest is expensive to evaluate and thus the sampling of the parameter space is necessarily small. As a result choosing a "good" set of samples at which to evaluate is crucial to glean as much information as possible from the fewest samples. While space-filling sampling designs such as Latin hypercubes provide a good initial cover of the entire domain, more detailed studies typically rely on adaptive sampling: Given an initial set of samples, these techniques construct a surrogate model and use it to evaluate a scoring function which aims to predict the expected gain from evaluating a potential new sample. There exist a large number of different surrogate models as well as different scoring functions each with their own advantages and disadvantages. In this paper we present an extensive comparative study of adaptive sampling using four popular regression models combined with six traditional scoring functions compared against a space-filling design. Furthermore, for a single high-dimensional output function, we introduce a new class of scoring functions based on global topological rather than local geometric information. The new scoring functions are competitive in terms of the root mean squared prediction error but are expected to better recover the global topological structure. Our experiments suggest that the most common point of failure of adaptive sampling schemes are ill-suited regression models. Nevertheless, even given well-fitted surrogate models many scoring functions fail to outperform a space-filling design.