For the difficult-to-formulate sub-systems, we would train a predictive phase stability classifier, using a featurisation of the experimental data as explained in the previous subsection. Details for how we trained this classifier are described in the SI. We would then use this classifier to predict the phase stability of each point in our candidate set, 𝐂, and apply a phase stability cut-off (between 0 and 1) to drop any points without a minimum probability of stability, to generate a restricted candidate set, 𝐂 * . This phase-stability cut-off would be modified on each iteration of the DoE as explained in the Results & Discussion section. For the other, more stable sub-systems, we kept the original candidate set. Finally, we used a greedy search algorithm to select the next batch of experiments out of the (restricted) candidate design to best augment the already collected experimental data based on the MaxPro criterion (using the MaxProAugment function). If 36 additional experiments are requested, instead of performing an expensive optimisation to simultaneously calculate the 36 best points, a one-ata-time greedy optimisation procedure sequentially suggests points 1 to 36. There is a small trade-off in optimality for substantially increased computational efficiency, as we wish to be able to generate designs on-the-fly in a high-dimensional design space for high-throughput experimental campaigns. The code for the complete method is provided in the SI.