Figure 1.

Overview of active learning framework for the single-objective optimization in this work. First, the alloys in the dataset are visualized with the Wasserstein autoencoder (WAE). Second, the alloys in the training dataset are trained with ensemble models comprised of neural networks and boosting trees. Third, different exploitation and exploration strategies are alternatively used to search for promising compositions in the test dataset. In the last step, the most promising compositions are selected and then fed back into the training dataset to initiate the next iteration. This figure is adapted from figure 1 in [50]. This framework is used to test the efficiency of the active learning strategies including pure exploitation, pure exploration, dependent and independent methods, respectively, for different dataset. The pure exploitation strategy prioritizes compositions with target mean values, such as those with low TEC for Invar alloys. Conversely, the pure exploration strategy seeks compositions with high uncertainty values to explore unknown regions. Independent methods conduct either exploration or exploitation in each iteration, while dependent methods combine both in each iteration. Further details of these methods are provided in Methods §2d.