Algorithm 2 MFGP—Bayesian Optimization

Require: Search space for optimization, $X^{*}$; MFGP prior with mean function, $\mu \left(\mathbf{x}\right)$ and kernel function, $k\left(\mathbf{x},{\mathbf{x}}^{\prime }\right)$; objective function, $J(t,P,v)$; number of optimization steps allowed, $N_{\mathrm{opt}}$; $N_H,N_L$, accepted tolerance for the melt pool depth, $ϵ$ 1:for$i\leftarrow 1$ to $N_{\mathrm{opt}}$ do 2:    if $|d(t,P,v)-d^{*}|<ϵ$ then 3:        Perform HF simulations at $\widehat{\mathbf{x}}={argmax}_{\mathbf{x}}EI\left(\mathbf{x}\right)$ 4:        Augment data with HF predictions, update MFGP 5:        Perform LF simulations at $\widehat{\mathbf{x}}={argmax}_{\mathbf{x}}GP-MI\left(\mathbf{x}\right)$ 6:        Augment data with LF predictions, update MFGP 7:    else 8:        break 9:    end if 10:end for