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Recent progress in machine learning methods, and the emerging availability ofprogrammable interfaces for scanning probe microscopes (SPMs), have propelledautomated and autonomous microscopies to the forefront of attention of thescientific community. However, enabling automated microscopy requires thedevelopment of task-specific machine learning methods, understanding theinterplay between physics discovery and machine learning, and fully defineddiscovery workflows. This, in turn, requires balancing the physical intuitionand prior knowledge of the domain scientist with rewards that defineexperimental goals and machine learning algorithms that can translate these tospecific experimental protocols. Here, we discuss the basic principles ofBayesian active learning and illustrate its applications for SPM. We progressfrom the Gaussian Process as a simple data-driven method and Bayesian inferencefor physical models as an extension of physics-based functional fits to morecomplex deep kernel learning methods, structured Gaussian Processes, andhypothesis learning. These frameworks allow for the use of prior data, thediscovery of specific functionalities as encoded in spectral data, andexploration of physical laws manifesting during the experiment. The discussedframework can be universally applied to all techniques combining imaging andspectroscopy, SPM methods, nanoindentation, electron microscopy andspectroscopy, and chemical imaging methods, and can be particularly impactfulfor destructive or irreversible measurements.

Bayesian Active Learning for Scanning Probe Microscopy: from Gaussian Processes to Hypothesis Learning