Active learning for noisy physical experiments with more than two responses

When designing experiments, one of the objectives consists in building a model for prediction of future observations. If the underlying phenomenon is complex, one option is to employ machine learning (ML) models for data analysis and to build accurate emulators that function as virtual representations of the physical process, and can be used in lieu of further evaluations of the actual physical system. However, to obtain accurate models, informative data must be provided to train the algorithms, and a typical approach consists in the sequential collection of data via active learning (AL) strategies. Most existing literature on AL focuses on computer experiments. In this paper we introduce an AL algorithm for Physical Experiments based on nonparametric Ranking and Clustering (ALPERC) that can be used for sequential data collection in noisy settings when three or more responses are investigated in the same experiment. We inspect the performance of the ALPERC algorithm through simulations and a case study application on the prediction of relevant properties of thermoelectric materials.