The Use of Radial Basis Function Surrogate Models for Sampling Process Acceleration in Bayesian Inversion

2019 ◽  
pp. 228-238 ◽  
Author(s):  
Simona Domesová
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Surrogate Models ◽  
Bayesian Inversion ◽  
Sampling Process ◽  
Radial Basis

scholarly journals Integration of expert knowledge into radial basis function surrogate models

2015 ◽  
Vol 17 (3) ◽  
pp. 577-603 ◽  
Author(s):  
Zuzana Nedělková ◽  
Peter Lindroth ◽  
Ann-Brith Strömberg ◽  
Michael Patriksson
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Expert Knowledge ◽  
Surrogate Models ◽  
Radial Basis

scholarly journals Sequential Optimization of Strip Bending Process Using Multiquadric Radial Basis Function Surrogate Models

2013 ◽  
Vol 554-557 ◽  
pp. 911-918 ◽  
Author(s):  
Jos Havinga ◽  
Gerrit Klaseboer ◽  
A.H. van den Boogaard
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Surrogate Model ◽  
Surrogate Modeling ◽  
Surrogate Models ◽  
Sequential Optimization ◽  
Global Response ◽  
Local Point ◽  
Bending Process ◽  
Radial Basis

Surrogate models are used within the sequential optimization strategy for forming processes. A sequential improvement (SI) scheme is used to refine the surrogate model in the optimal region. One of the popular surrogate modeling methods for SI is Kriging. However, the global response of Kriging models deteriorates in some cases due to local model refinement within SI. This may be problematic for multimodal optimization problems and for other applications where correct prediction of the global response is needed. In this paper the deteriorating global behavior of the Kriging surrogate modeling technique is shown for a model of a strip bending process. It is shown that a Radial Basis Function (RBF) surrogate model with Multiquadric (MQ) basis functions performs equally well in terms of optimization efficiency and better in terms of global predictive accuracy. The local point density is taken into account in the model formulation.

scholarly journals Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

2021 ◽  
Vol 26 (2) ◽  
pp. 31
Author(s):  
Manuel Berkemeier ◽  
Sebastian Peitz
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Optimization Problems ◽  
Trust Region ◽  
Surrogate Models ◽  
Descent Method ◽  
Information Need ◽  
Derivative Free ◽  
Radial Basis ◽  
General Scalar

We present a local trust region descent algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. Convergence to a Pareto critical point is proven. The method is derivative-free in the sense that derivative information need not be available for the expensive objectives. Instead, a multiobjective trust region approach is used that works similarly to its well-known scalar counterparts and complements multiobjective line-search algorithms. Local surrogate models constructed from evaluation data of the true objective functions are employed to compute possible descent directions. In contrast to existing multiobjective trust region algorithms, these surrogates are not polynomial but carefully constructed radial basis function networks. This has the important advantage that the number of data points needed per iteration scales linearly with the decision space dimension. The local models qualify as fully linear and the corresponding general scalar framework is adapted for problems with multiple objectives.

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