Bayesian Optimization for Materials Science (eBook)

Preface 6
Contents 8
1 Overview of Bayesian Optimization in Materials Science 10
1.1 Brief Overview of Bayesian Optimisation 10
1.2 Examples of Bayesian Optimisation in Materials Science 13
1.2.1 Prediction of Compounds with Low Thermal Conductivity 13
1.2.2 Prediction of Compounds with Optimal Melting Temperatures and Elastic Properties 14
1.2.3 Prediction of Interface Structures 15
1.2.4 Design of Interface Nanostructure 16
1.3 Bayesian Optimization Requires Good Feature Vectors 17
References 19
2 Theory of Bayesian Optimization 20
2.1 Bayesian Interpretation of Probability 20
2.2 Equilibrium Bond Lengths Via Bayesian Optimization 21
2.2.1 Prior Probability 23
2.2.2 Likelihood Function and Posterior Distribution 24
2.2.3 Example Calculation of the Posterior Distribution 26
2.2.4 The Expected Improvement 27
2.2.5 Example Run of Bayesian Optimisation 28
2.2.6 Training 31
2.3 Bayesian Optimization in the General Case 32
2.4 R Code for Bayesian Optimization 33
Appendix 2.1 34
Appendix 2.2 35
Appendix 2.3 36
References 37
3 Bayesian Optimization of Molecules Adsorbed to Metal Surfaces 38
3.1 Density Functional Theory for Surface Science 38
3.2 Bayesian Optimization for Surface Science 40
3.2.1 Preliminary Computational Study 41
3.2.2 Statement of Optimization Problem 43
3.2.3 Data Description 44
3.2.4 Choice of Feature Vectors 45
3.2.5 Training of Hyperparameters 46
3.2.6 Predictive Performance 48
3.2.7 Discussion 49
References 50