Table 3 Bayesian Optimization Algorithm.
From: Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables
(0) Generate initial dataset \({{\boldsymbol{D}}}_{0}\) (1) For n = 1, 2, …, do |
(2) Fit the latent variable GP model \({\hat{{\boldsymbol{y}}}}_{{\boldsymbol{n}}}({\boldsymbol{x}};{{\boldsymbol{D}}}_{{\boldsymbol{n}}{\boldsymbol{-}}1})\) |
(3) Select the next sampling point \({{\boldsymbol{x}}}_{{\boldsymbol{n}}{\boldsymbol{+}}1}\) by maximizing EI: |
\({{\boldsymbol{x}}}_{{\boldsymbol{n}}{\boldsymbol{+}}1}={\bf{\arg }}\mathop{{\bf{m}}{\bf{a}}{\bf{x}}}\limits_{{\boldsymbol{x}}}{\boldsymbol{EI}}({\boldsymbol{x}};{\hat{{\boldsymbol{y}}}}_{{\boldsymbol{n}}})\) |
(4) Query simulations/experiments to obtain \({{\boldsymbol{y}}}_{{\boldsymbol{n}}{\boldsymbol{+}}1}\) |
(5) Augment data \({{\boldsymbol{D}}}_{{\boldsymbol{n}}{\boldsymbol{+}}1}=\{{{\boldsymbol{D}}}_{{\boldsymbol{n}}},\,({{\boldsymbol{x}}}_{{\boldsymbol{n}}{\boldsymbol{+}}1},{{\boldsymbol{y}}}_{{\boldsymbol{n}}{\boldsymbol{+}}1})\}\) |
(6) End for. |
