## 3 Demonstration Problem: Design of Aluminum Foam-Cored Sandwich Panel
### Comparison of Results with Traditional IDEM  
To discuss the usefulness of the presented active learning method, the feasible regions obtained in this study were compared to the results in traditional IDEM. In this way, the accuracy of the feasible region and the total samples required in the presented method were compared with the results in traditional IDEM. Figure 11 compares the results obtained by traditional IDEM (left) and active learning (right). The feasible region in traditional method is identified in the gridded input space (core density-thickness level) with a total sample size of 4941, that is composed of resolutions of 0.2 mm in thickness and 0.005 g/cm\({}^{3}\) in density. It can be observed that the exhaustive grid sample points were evaluated, but a large number of sample points were expended in evaluating unsatisfactory design points, which is clearly inefficient. On the other hand, the feasible region determined by SVM active learning algorithm was obtained with only 236 samples, which is much fewer yet almost identical to the true boundary.  
Figure 12 also shows the comparison results obtained by traditional IDEM (left) and active learning (right) at processing level. The sample size of traditional IDEM was 4131 and composed of the resolutions of 1 s in holding time and 0.02 wt% in amount of TiH\({}_{2}\), whereas only 226 samples were required in active learning. Again, the accuracy of the SVM is evident with much less sampling effort.  
As explained earlier, the initial training samples were chosen randomly, meaning that the initial SVM boundaries vary, and the total sample sizes for the final SVM to meet the accuracy criteria may be greater or smaller than those presented in this study. For example, after repeatedly running the algorithm 5 times with the same stopping criteria, it was found to have a relatively small variation in the total sample sizes (295, 175, 229, 207, and 239, respectively), which indicates the algorithm performs in a reasonably robust fashion.  
In traditional IDEM, following the evaluation of the discretized input space, a numerical root finding method is used to determine the exact border of the feasible region boundary located between pairs of feasible and infeasible points. This representation of feasible regions is solely dependent on the gridded input space determined by discretizing resolution. A coarse discretization can cause a rough estimate of the feasible region composed of relatively fewer boundary points leading to some input points that are considered as satisfying but may be unsatisfactory if much finer discretization is undertaken. Furthermore, it is even more difficult in the case of arbitrary or multiple isolated shapes of the true boundary. This discretization error can be alleviated by increasing the resolution of discretization, which will, however, increase the amount of computation required.  
Figure 10: Feasible region at processing level.  
In this study, the deflection caused by the blast impact was evaluated using a kriging surrogate model; however, there may be a situation where surrogate models cannot be accepted. For example, when assuming the total 4941 samples and performing the blast impact simulations with the approximate running time of 30 min each, the total time consumed for simulations was roughly 2470 h \(\approx\) 103 d with traditional IDEM, which is clearly time-consuming. Meanwhile, the total time for the presented method would take 118 h \(\approx\) 5 d, which is time-saving and plausible. Overall, the comparison results indicate that the presented IDEM with active learning can significantly reduce the sample size required for identification of a feasible region.