The nature of statistical learning theory
The nature of statistical learning theory
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Fast Evaluation of Radial Basis Functions: Methods for Generalized Multiquadrics in $\RR^\protectn$
SIAM Journal on Scientific Computing
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models
A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models
Journal of Global Optimization
Metamodeling using extended radial basis functions: a comparative approach
Engineering with Computers
Artificial Neural Networks
Various approaches for constructing an ensemble of metamodels using local measures
Structural and Multidisciplinary Optimization
Ensemble of surrogates with recursive arithmetic average
Structural and Multidisciplinary Optimization
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The determination of complex underlying relationships between system parameters from simulated and/or recorded data requires advanced interpolating functions, also known as surrogates. The development of surrogates for such complex relationships often requires the modeling of high dimensional and non-smooth functions using limited information. To this end, the hybrid surrogate modeling paradigm, where different surrogate models are combined, offers an effective solution. In this paper, we develop a new high fidelity surrogate modeling technique that we call the Adaptive Hybrid Functions (AHF). The AHF formulates a reliable Crowding Distance-Based Trust Region (CD-TR), and adaptively combines the favorable characteristics of different surrogate models. The weight of each contributing surrogate model is determined based on the local measure of accuracy for that surrogate model in the pertinent trust region. Such an approach is intended to exploit the advantages of each component surrogate. This approach seeks to simultaneously capture the global trend of the function as well as the local deviations. In this paper, the AHF combines four component surrogate models: (i) the Quadratic Response Surface Model (QRSM), (ii) the Radial Basis Functions (RBF), (iii) the Extended Radial Basis Functions (E-RBF), and (iv) the Kriging model. The AHF is applied to standard test problems and to a complex engineering design problem. Subsequent evaluations of the Root Mean Squared Error (RMSE) and the Maximum Absolute Error (MAE) illustrate the promising potential of this hybrid surrogate modeling approach.