[BANANA] Berkeley Lab - Computing Sciences Seminar - Wednesday, 7/1/2009, 11:30am

[Esmond G. Ng]

Berkeley Lab - Computing Sciences Seminar

/Date/:

    Wednesday, July 1, 2009

/Time/:

    11:30am - 12:30pm

/Location/:

    Bldg. 50F, Room 1647

/Speaker/:

    Christine A. Shoemaker, Joseph P. Ripley Professor
    School of Civil and Environmental Engineering
    School of Operations Research and Information Engineering
    Cornell University

/Title/:

    New RBF Algorithms for Nonlinear and Global Optimization and
    Uncertainty Analysis of Computationally Expensive Simulation Models

/Abstract/:

    Optimization and uncertainty analyses used in conjunction with
    complex simulation models are important for using models to make
    predictions based on observations and for finding optimal designs or
    policies. Global Optimization and uncertainty analysis typically
    require a very large number of simulations, often thousands or tens
    of thousands. However, this approach is not feasible for
    computationally expensive simulation models that arise in DOE
    applications.

    Our approach to creating more efficient methods for this analysis is
    to iteratively approximate the objective function or likelihood
    function /f(x)/. All of our methods are derivative-free and can be
    applied to systems of nonlinear partial differential equations as
    well as multimodal functions.

    Our methods differ from most other methods in that we use the
    results of most previous simulations in the optimization search in
    each iteration to help build an approximation of the function to be
    optimized in future optimization iterations. In iteration /m/, the
    RBF then approximates /f(x)/ based upon the /m/ values of /f(x_i)/
    for /x_1/, /x_2/, ..., /x_m/ computed in previous iterations of the
    optimization search.

    It is this use of previously evaluated points /f(x_i)/ that is
    responsible for great savings in computational time. I will review
    several optimization methods we have developed including a local
    optimization method ORBIT (that uses trust regions) and two global
    optimization methods, Stochastic RBF and GORBIT. Stochastic RBF has
    also been modified to run in parallel. GORBIT uses a new multi-start
    method in combination with a modified version of ORBIT that uses
    previous simulations from other starts to develop the trust region.
    I will give results that compare these algorithms and show
    significant computational improvements over other methods multiple
    problems, including complex simulations.

    I will also briefly discuss the use of these derivative-based
    methods in our new uncertainty method SOARS that combines an
    iterative RBF approximation of the multivariate likelihood function
    , iterative optimization search, and Markov Chain Monte Carlo.
    Results show that the computation required by SOARS is less than
    1/60 of that required by standard Markov Chain Monte Carlo for
    accurate uncertainty assessment on two very different engineering
    applications.

/Additional Notes/:

    This talk is based primarily on work done jointly with R. Regis and
    S. Wild in manuscripts and in papers published in INFORMS Jn. of
    Computing, European Jn. of Operations Research, Jn. of Computational
    and Graph. Statistics, and SIAM Scientific Computing as well as the
    Ph.D. theses of Regis and Wild.

/Host of Seminar/:

    Juan Meza


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