Computer Experiments for Function Approximations

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Description

This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space ... continued below

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PDF-file: 68 pages; size: 2.6 Mbytes

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Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O & Tong, C October 15, 2007.

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Description

This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.

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PDF-file: 68 pages; size: 2.6 Mbytes

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  • Report No.: UCRL-TR-235618
  • Grant Number: W-7405-ENG-48
  • DOI: 10.2172/923129 | External Link
  • Office of Scientific & Technical Information Report Number: 923129
  • Archival Resource Key: ark:/67531/metadc896779

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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Creation Date

  • October 15, 2007

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

Description Last Updated

  • Nov. 23, 2016, 11:20 a.m.

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Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O & Tong, C. Computer Experiments for Function Approximations, report, October 15, 2007; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc896779/: accessed December 13, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.