Use of Kriging Models to Approximate Deterministic Computer Models

By Jay D. Martin, Timothy W. Simpson. 2005

908 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/470dea3077d6a971ceb31b98dd16a56d4fb0f8cc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Kwang‐Yong Kim
2. David Ginsbourger
3. Ki-Don Lee
4. Jack P. C. Kleijnen
5. Peretz P. Friedmann
6. A. Afzal
7. S. Shan
8. G. G. Wang

In Computational Theory and Mathematics

1. David Ginsbourger
2. G. G. Wang
3. S. Shan
4. Kwang‐Yong Kim
5. Daniel W. Apley
6. V. Roshan Joseph
7. Rohit Tripathy
8. Jack P. C. Kleijnen

In Management Science and Operations Research

1. Kwang‐Yong Kim
2. David Ginsbourger
3. S. Shan
4. G. G. Wang
5. Daniel W. Apley
6. V. Roshan Joseph
7. Jack P. C. Kleijnen
8. Ki-Don Lee

Citations in the corpus

• A non‐stationary covariance‐based Kriging method for metamodelling in engineering design (2007, methodology): “[29] compared the use of the MLE and the CV.”
• Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions (2010, background): “Wang and Shan (2007) listed popular models, such as kriging models (Joseph et al. 2006; Martin and Simpson 2005), radial basis functions (RBF) models (Fang and Horstemeyer 2006; Regis and Shoemaker 2007a, b), response surface models (Hill and Hunter 1966; Kaufman et al.”
• Kriging is well-suited to parallelize optimization (2010, positive): “Recent works [17, 30, 31] illustrate the practical relevance of Kriging to approximate computer codes in application areas such as aerospace engineering or materials science.”
• ORTHOGONAL-MAXIMIN LATIN HYPERCUBE DESIGNS (2008, background): “Simulations carried out by Martin and Simpson (2005) show that universal kriging can improve the prediction over ordinary kriging.”
• Reduced-Order Nonlinear Unsteady Aerodynamic Modeling Using a Surrogate-Based Recurrence Framework (2010, methodology): “With ̂(2)var and
  ̂ known, pk are found such that a likelihood function is maximized [28,34].”
• Kriging metamodeling in simulation: A review (2009, methodology): “More recent are the references 17 through 21 in [38].”
• Update strategies for kriging models used in variable fidelity optimization (2006, methodology): “There are two main methods of estimating these parameters (Martin and Simpson 2005): cross-validation andmaximum likelihood estimation (MLE).”
• Optimization of a Cylindrical Film Cooling Hole using Surrogate Modeling (2009, methodology): “The weighted average surrogate model consists of a polynomial response surface approximation model (RSA) [ 13 ], Kriging meta-modeling technique (KRG) [ 14 ] and radial basis neural network (RBNN) [ 15 ].”
• Ensemble of metamodels with optimized weight factors (2008, methodology): “There are many metamodeling techniques including polynomial response surface (PRS) approximations (Myers and Montgomery 2002), multivariate adaptive regression splines (Friedman 1991), radial basis functions (RBF; Hardy 1971; Dyn et al. 1986; Mullur and Messac 2004), Kriging (KR; Sacks et al. 1989; ”
• Multi-objective optimization of solar air heater with obstacles on absorber plate (2015, methodology): “Kriging model The Kriging method (Martin and Simpson, 2005; Raza and Kim, 2008) in its basic formulation estimates the value of a function (response) at some unsampled location as a combination of two components: a global model and a systematic departure.”
• Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2019, methodology): “Traditional choices for surrogate models include Gaussian process regression (GPR) (or Kriging) [15, 16, 17, 18, 19], polynomial chaos expansion [20, 21, 22, 23], and radial basis functions [24, 25].”
• Surrogate-based Analysis and Optimization (2005, neutral): “7 and Kriging [58].”
• Optimization of pulsatile flow and geometry of a convergent–divergent micromixer (2015, methodology): “The Kriging (KRG) model [29] can be formulated as a combination of two components, the global model and a systematic departure,”
• Review of Metamodeling Techniques in Support of Engineering Design Optimization (2007, methodology): “is computed for the additional validation points, which differs from the traditional use of R square [61].”
• Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, background): “, data assimilation [264]–[269], parameter identification [270]–[273], uncertainty quantification [274]–[280], optimization and control [281]–[288]).”