Global response approximation with radial basis functions

Fang, Hsu Wei; Horstemeyer, M.F.

doi:10.1080/03052150500422294

Cited by 190 publications

(108 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The Radial Basis Function (RBF) can be expressed by the linear combination of the functions in terms of radial distance from the considered point to every interpolation point (or sample point or experiment design point) [12]:…”

Section: Rbf and Augmented Rbf Methodsmentioning

confidence: 99%

See 1 more Smart Citation

An efficient global optimization algorithm based on augmented radial basis function

Sui

Shanpo

Guo

2008

Int. J. Simul. Multidisci. Des. Optim.

View full text Add to dashboard Cite

-In the structural optimization, the accuracy of approximation for the established mathematical model will directly affect the solution efficiency, even the convergence. The global optimization model based on the augmented Gaussian radial basis function h as a high approximation accuracy, but the solution efficiency will not be increased without a matched optimization algorithm. In this paper, we adopt the information at the interpolating points in large extent and the augmented Gaussian radial basis function to construct the approximate mathematical model. Using the explicit derivatives of the model for the sensitivities and sequential quadratic programming (SQP) algorithm for the optimization solving, an efficient algorithm of global optimization is proposed. It is simple to be realized and converges quickly. Two examples will illustrate the stability and efficiency of the present algorithm.

show abstract

Section: Rbf and Augmented Rbf Methodsmentioning

confidence: 99%

“…Fang and Horstemeyer [12] demonstrate that the approximation accuracy of the augmented Gaussian RBF is higher than that of other types of RBF and its approximation domain is also wider. How to solve this type of models with high approximation accuracy?…”

Section: Introductionmentioning

confidence: 99%

An efficient global optimization algorithm based on augmented radial basis function

Sui

Shanpo

Guo

2008

Int. J. Simul. Multidisci. Des. Optim.

View full text Add to dashboard Cite

show abstract

“…A wide variety of techniques have been discussed in the literature for creating the metamodels [14]. These techniques include response surface modelling [9], Radial Basis Functions ( [2]; [3]), Multivariate Adaptive Regression Splines [4] and Support Vector Machine [15]. In this study, a Gaussian stochastic process (Gasp) model was investigated as an alternative technique for approximating a borehole computer model.…”

Section: Modelling Borehole Computer Experimentsmentioning

confidence: 99%

Study of Increased Usage for Government Services and Customer Interface Using Mobile Apps

Гупта¹,

Menon²

2017

IJAST

View full text Add to dashboard Cite

show abstract

“…Steps (2) and (3) are often coupled and considered in line with each other since learning/fitting techniques have evolved to be highly specific and dependent on the metamodel used. Examples of popular metamodels include polynomials (Montgomery, 2008), Kriging (Sacks et al, 1989), neural networks (Cheng and Titterington, 1994), radial basis functions (Fang and Horstemeyer, 2006;Regis and Shoemaker, 2013), multivariate adaptive regression splines (Friedman, 1991), and inductive learning (Wang and Shan, 2007).…”

Section: Metamodelingmentioning

confidence: 99%

Statistical metamodeling of dynamic network loading

Song

Han

Wang

2018

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses the dynamics of flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator, which maps a set of path departure rates to a set of path travel times. It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, non-differentiability, non-monotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult problem, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging. We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, while possessing closed-form Jacobians. The implications of these desirable properties for DTA research and model applications are discussed in depth.

show abstract

Global response approximation with radial basis functions

Cited by 190 publications

References 16 publications

An efficient global optimization algorithm based on augmented radial basis function

An efficient global optimization algorithm based on augmented radial basis function

Study of Increased Usage for Government Services and Customer Interface Using Mobile Apps

Statistical metamodeling of dynamic network loading

Contact Info

Product

Resources

About