Algorithm 1 Active GP Entropy-Based Sampling Algorithm

$$\begin{array}{cc}\hfill & \mathbf{Input}:{\mathit{X}}_{{\mathcal{A}}_0},{\mathit{y}}_{{\mathcal{A}}_0},\mathcal{V},{\mathit{X}}_{\mathcal{V}},N,\text{method}\hfill \\ \hfill & \mathrm{Output}:\mathcal{A}\hfill \\ \hfill & 1\text{Obtain estimated field}{\widehat{\psi }}_{\mathcal{V}}\text{by taking the mean of (2) (for}\hfill \\ \hfill & {\text{GPE and GPE}}_{\mu })\text{or}(18)(\text{for WGPE});\hfill \\ \hfill & 2\text{Set}n=n_0\text{and}\mathcal{A}={\mathcal{A}}_0;\hfill \\ \hfill & 3\mathbf{while}n\le N\mathbf{do}\hfill \\ \hfill & 4\mid \begin{array}{c}\mathbf{for}\ell \in \mathcal{V}\setminus \mathcal{A}\mathbf{do}\hfill \\ \mid \begin{array}{c}\text{Compute}{\delta }_{\psi ,\ell }\text{using (9) or (15) or (20) based on}\hfill \\ \text{method};\hfill \end{array}\phantom{\mid }\hfill \\ \mathbf{end}\hfill \\ {\ell }^{\ast }=\text{arg}{\max }_{\ell }{\delta }_{\widehat{\psi },\ell };\hfill \\ \text{Get MEP sample}{y}_{{\ell }^{\ast }}\text{at location}{\mathit{x}}_{{\ell }^{\ast }};\hfill \\ \mathcal{A}=\mathcal{A}\cup \{{\ell }^{\ast }\};\hfill \\ \mathcal{V}=\mathcal{V}-\{{\ell }^{\ast }\};\hfill \\ \text{Obtain estimated field}{\widehat{\psi }}_{\mathcal{V}}\text{by taking the mean of (2)}\hfill \\ \text{or}(18);\hfill \\ \text{Increment n};\hfill \end{array}\phantom{\mid }\hfill \\ \hfill & 13\mathbf{end}\hfill \\ \hfill & 14\mathbf{return}\mathcal{A};\hfill \end{array}$$