Surrogate Modeling and Optimization : Theories, Applications, and Limitations.

Format:

Book

Author/Creator:

Kim, Nam-ho.

Language:

English

Subjects (All):

Mathematical models.

Physical Description:

1 online resource (462 pages)

Edition:

1st ed.

Place of Publication:

Newark : John Wiley & Sons, Incorporated, 2026.

Summary:

An expert reference on building surrogate models, using them for optimization, their associated prediction uncertainty, and potential failures, with practical implementation in MATLAB Surrogate Modeling and Optimization explains the meaning of different surrogate models and provides an in-depth understanding of such surrogates, emphasizing how.

Contents:

Cover

Title Page

Copyright Page

Dedication Page

Contents

Preface

Acknowledgment

About the Companion Website

Part I Basics of Surrogate Modeling

Chapter 1 Introduction to Surrogate Models

1.1 What Is Surrogate Modeling?

1.2 Surrogate Models

1.3 Design of Experiments: Sampling

1.4 Interpolation Versus Extrapolation

1.5 Flowchart of Surrogate Modeling

1.6 Overview of Surrogate Modeling

1.7 Smoothness and Loss Function

Chapter 2 Polynomial Response Surfaces

2.1 Introduction

2.2 Curve Fitting

2.3 Linear Regression

2.3.1 Polynomial Response Surface

2.3.2 Polynomial Response Surface in Multiple Dimensions

2.3.3 Curse of Dimensionality

2.3.4 Assumptions in Linear Regression

2.4 Goodness of Fit

2.4.1 Estimation of Noise in Samples

2.4.2 Coefficient of Multiple Determination

2.4.3 Cross-validation

2.5 Confidence of Coefficients and Backward Elimination

2.6 Prediction Variance

2.6.1 Prediction Uncertainty

2.6.2 Sample Sensitivity

2.6.3 Prediction Variance with Variable Noise

2.7 Outliers

2.8 Statistical View of Linear Regression

Chapter 3 Design of Experiments

3.1 Introduction

3.2 Design of Experiments in Box-like Domains

3.2.1 Scaling of Input Variables

3.2.2 Interpolation, Extrapolation, and Prediction Variance

3.2.3 Designs for Linear Polynomial Response Surfaces

3.2.4 Designs for Quadratic Polynomial Response Surfaces

3.3 Optimal Design of Experiments

3.3.1 D-Optimal Design

3.3.2 A-Optimal Design

3.3.3 G-Optimal Design

3.3.4 Minimum Bias Design

3.4 Space-Filling Design of Experiments

3.4.1 Monte Carlo Simulation

3.4.2 Latin Hypercube Sampling

3.4.3 Orthogonal Arrays

3.5 Review of Various Designs of Experiments

3.5.1 Guideline for Selecting Designs of Experiments.

3.5.2 Good Practice for Design of Experiments

Part II Design Optimization

Chapter 4 Optimization Definition and Formulation

4.1 Introduction

4.2 Design Optimization Definition

4.2.1 Design Optimization Process

4.2.2 Design Variables and Feasible Domain

4.2.3 Graphical Optimization

4.3 Optimization Problem Formulation

4.3.1 Three-step Problem Definition

4.3.2 Standard Form

4.3.3 Normalization

4.3.4 Convex Function and Convex Problem

4.4 Optimality Criteria

4.4.1 Global Versus Local Optimum

4.4.2 Unconstrained Optimization

4.4.3 Constrained Optimization

4.4.4 Effect of Constraint Limit

4.4.5 Sensitivity of Optimum Solution to Parameters

Chapter 5 Numerical Optimization Algorithms

5.1 Introduction

5.2 Overview of the Numerical Optimization Process

5.3 Determination of Step Size

5.3.1 Descent Direction

5.3.2 Step-Size Termination Criterion

5.3.3 Interval Reduction Method

5.3.4 Quadratic Interpolation Method

5.4 Unconstrained Optimization Algorithms

5.4.1 Steepest Descent Method

5.4.2 Conjugate Gradient Method

5.4.3 Newton Method

5.4.4 Quasi-Newton Method

5.4.5 Rate of Convergence

5.5 Constrained Optimization Using Unconstrained Algorithms

5.5.1 Lagrange Multiplier Method

5.5.2 Penalty Function Method

5.6 Constrained Optimization Using Direct Methods

5.6.1 Sequential Linear Programming (SLP) Method

5.6.2 Quadratic Programming (QP) Subproblem

5.6.3 Constrained Steepest Descent Method

5.6.4 Feasible Direction Method

5.6.5 Constrained Quasi-Newton Method

5.7 Matlab Optimization Toolbox

5.8 Practical Suggestions for Numerical Optimization

Chapter 6 Global Search Optimization Algorithms

6.1 Introduction

6.2 Nelderâ€"Mead Sequential Simplex Algorithm

6.3 DIRECT Method

6.3.1 Lipschitzian Optimization.

6.3.2 DIRECT in 1D

6.3.3 DIRECT Algorithm

6.4 Genetic Algorithms

6.4.1 Representation of Design

6.4.2 Genetic Operators

6.4.3 Procedure of Genetic Algorithms

6.4.4 Genetic Algorithm in Matlab

6.4.5 When to Use Genetic Algorithm?

6.5 Particle Swarm Optimization

6.6 Simulated Annealing Optimization

Part III Advanced Topics in Surrogate Modeling

Chapter 7 Kriging Surrogateâ€"Gaussian Process Model

7.1 Introduction

7.2 Kriging Philosophy

7.2.1 Correlation Between Two Random Variables

7.2.2 Kriging Surrogate Approximation

7.2.3 Correlation Model

7.3 Kriging Surrogate Model

7.3.1 Global Function and Distribution of Errors

7.3.2 Local Departure

7.3.3 Hyperparameters and Likelihood Function

7.4 Issues in Determining Hyperparameters

7.4.1 Lower and Upper Bounds of Hyperparameter

7.4.2 Finding Optimum Value of Hyperparameter

7.4.3 Issues Related to the Number of Samples

7.4.4 Computational Cost of Kriging Surrogate

7.4.5 Hyperparameter and Extrapolation Accuracy

7.4.6 Uncertainty in Kriging Predictions

7.4.7 Effect of Global Function

7.5 Numerical Implementation of Kriging Surrogate

7.6 Kriging with Nuggetsâ€"Fitting with Noisy Data (Gaussian Process Regression)

7.6.1 Kriging Surrogate with Correlated Noise

7.6.2 Kriging Surrogate with Homogeneous Noise

Chapter 8 Neural Network Model

8.1 Introduction

8.2 Feedforward Neural Network Model

8.2.1 Concept of Feedforward Neural Network

8.2.2 Feedforward Mechanism

8.2.3 Activation Functions

8.2.4 Backpropagation Process

8.3 Matlab Functions for Feedforward Neural Network

8.4 Uncertainty Quantification in Neural Network Models

8.4.1 Training Uncertainty

8.4.2 Sampling Uncertainty

8.4.3 Confidence Intervals and Prediction Intervals

8.5 Issues in Feedforward Neural Network.

8.5.1 Adaptive Learning Rate

8.5.2 Scaling Input Data

8.5.3 Overfitting

8.6 Neural Networks with Constraints

8.6.1 Penalty Method for Constraints

8.6.2 Regularization Using Soft-maximum

8.6.3 Backpropagation of Penalty Constraints

8.6.4 Updating Penalty Parameter

8.6.5 Numerical Examples

Chapter 9 Multi-fidelity Surrogate Models

9.1 Introduction

9.2 Multi-fidelity Surrogate Models

9.3 Regression-based Multi-fidelity Surrogate

9.4 Kriging-based Multi-fidelity Surrogate

9.4.1 Multi-fidelity Surrogate with Low-fidelity Function

9.4.2 Multi-fidelity Surrogate with Low-fidelity Samples

9.5 Sampling Strategy for Multi-fidelity Surrogate Modeling

9.5.1 Selecting Locations for LF and HF Samples

9.5.2 Allocating LF and HF Samples

9.6 Challenges and Recommendations

9.6.1 Deciding Whether to Use LF Samples

9.6.2 Choosing Between Multiple LF Datasets

9.6.3 Selecting ρ for Other Surrogates

9.6.4 Recommendations on Using MF Surrogates

Exercise

Chapter 10 Efficient Global Optimization

10.1 Introduction

10.2 Efficient Global Optimization

10.2.1 Expected Improvement

10.2.2 Probability of Improvement

10.2.3 Adaptive Target for Probability of Improvement

10.2.4 Expected Feasibility

10.3 Efficient Global Optimization Using Polynomial Response Surface

10.4 Efficient Global Optimization Using Kriging Surrogate

References

Index

EULA.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

1-394-24584-X

1-394-24583-1

9781394245833

OCLC:

1565282844