ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions

Wild, Stefan M.; Regis, Rommel G.; Shoemaker, Christine A.

doi:10.1137/070691814

Cited by 206 publications

(153 citation statements)

References 27 publications

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“…Data-fit models include response surface methods that use interpolation or regression of simulation data to fit a model for the system output as a function of the parameters. In the statistical literature, Gaussian processes have been used extensively as data-fit surrogates for complex computational models [140], while data-fit surrogate approaches in optimization include polynomial response surfaces [85,108,137,216], radial basis functions [224], and Kriging models [204]. Stochastic spectral approximations, commonly used in uncertainty quantification, are another form of response surface model.…”

Section: Parametric Model Reduction and Surrogate Modelingmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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Abstract. Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for which the equations governing the system behavior depend on a set of parameters. Examples include parameterized partial differential equations and large-scale systems of parameterized ordinary differential equations. The goal of parametric model reduction is to generate low-cost but accurate models that characterize system response for different values of the parameters. This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lends insights to potential advantages and disadvantages in applying each of the methods. We highlight the important role played by parametric model reduction in design, control, optimization, and uncertainty quantification-settings that require repeated model evaluations over different parameter values.

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Section: Parametric Model Reduction and Surrogate Modelingmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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“…Radial basis function (RBF) interpolation (Wendland 2005) and Kriging interpolation (Lophaven et al 2002) are widely used to model multivariate functions and often yield good global representations of the unknown functions; see Buhmann (2003). Local and global optimization methods based on RBF interpolation can be studied in Wild et al (2008) and Gutmann (2001), respectively.…”

Section: Previous Workmentioning

confidence: 99%

Efficient solution of many instances of a simulation-based optimization problem utilizing a partition of the decision space

et al. 2017

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This paper concerns the solution of a class of mathematical optimization problems with simulation-based objective functions. The decision variables are partitioned into two groups, referred to as variables and parameters, respectively, such that the objective function value is influenced more by the variables than by the parameters. We aim to solve this optimization problem for a large number of parameter settings in a computationally efficient way. The algorithm developed uses surrogate models of the objective function for a selection of parameter settings, for each of which it computes an approximately optimal solution over the domain of the variables. Then, approximate optimal solutions for other parameter settings are computed through a weighting of the surrogate models without requiring additional expensive function evaluations. We have tested the algorithm's performance on a set of global optimization problems differing with respect to both mathematical properties and numbers of variables and parameters. Our results show that it outperforms a standard and often applied approach based on a surrogate model of the objective function over the complete space of variables and parameters.

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“…For the conjugate gradient or quasi-Newton approach, Cheng et al [2003] and Oyerinde et al [2009] are examples. Derivative-free local optimization methods exist such as optimization by radial basis function interpolation in trustregions (ORBIT) [Wild et al, 2008] Suwartadi et al [2010]. All local optimization methods will stop at the first local minimum found, which depends on the initial starting value of the search.…”

Section: Literature Reviewmentioning

confidence: 99%

Estimation of plume distribution for carbon sequestration using parameter estimation with limited monitoring data

Espinet

Shoemaker

Doughty

2013

Water Resources Research

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[1] This study develops and evaluates an integrated methodology including parameter zonation, efficient global optimization, and multiple aquifer realizations that gives a useful forecast of the pressure distribution and the CO 2 plume migration through a heterogeneous storage formation, over time, using only a few monitoring locations in a feasibly short amount of computing time, while dealing with data error. Geological characteristics of the example application are similar to a CO 2 sequestration pilot test conducted in a fluvialdeltaic geological setting. In the example, the CO 2 injection problem is simulated with the TOUGH2 code, a numerical simulator for multiphase (gas and aqueous), multicomponent flow and transport. The inverse problem is difficult because the GCS optimization estimation problem has multiple local minima and the simulation is computationally expensive. The efficient surrogate response surface global optimization algorithm ''Stochastic RBF'' (stochastic radial basis function) is used to calibrate the model parameters. Results are averaged over three saline aquifer realizations. In the third numerical experiment using only pressure data, the CO 2 plume could be determined with an average correlation coefficient compared to the actual plume of up to R 2 ¼ 0.916 (for current plume at t ¼ 1.5 years) and average R 2 ¼ 0.80 (for forecasted plume estimated at t ¼ 7.5 years years, using only the first 1.5 years of monitoring data). Adding gas saturation data improved the 6 year forecast somewhat (increasing average R 2 ¼ 0.85) but it was not significantly helpful in estimating the current plume. Both our inverse methodology and findings can be broadly applicable to GCS in heterogeneous sedimentary formations.Citation: Espinet, A., C. Shoemaker, and C. Doughty (2013), Estimation of Plume distribution for carbon sequestration using parameter estimation with limited monitoring data, Water Resour. Res., 49,

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ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions

Cited by 206 publications

References 27 publications

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Efficient solution of many instances of a simulation-based optimization problem utilizing a partition of the decision space

Estimation of plume distribution for carbon sequestration using parameter estimation with limited monitoring data

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