  Atomic arrangements and local sub-structures fundamentally influence emergent
material functionalities. The local structures are conventionally probed using
spatially resolved studies and the property correlations are usually deciphered
by a researcher based on sequential explorations and auxiliary information,
thus limiting the throughput efficiency. Here we demonstrate a Bayesian deep
learning based framework that automatically correlates material structure with
its electronic properties using scanning tunneling microscopy (STM)
measurements in real-time. Its predictions are used to autonomously direct
exploration toward regions of the sample that optimize a given material
property. This autonomous method is deployed on the low-temperature ultra-high
vacuum STM to understand the structure-property relationship in a
europium-based semimetal, EuZn2As2, one of the promising candidates for
studying the magnetism-driven topological properties. The framework employs a
sparse sampling approach to efficiently construct the scalar-property space
using a minimal number of measurements, about 1 - 10 % of the data required in
standard hyperspectral imaging methods. We further demonstrate a
target-property-guided active learning of structures within a multiscale
framework. This is implemented across length scales in a hierarchical fashion
for the autonomous discovery of structural origins for an observed material
property. This framework offers the choice to select and derive a suitable
scalar property from the spectroscopic data to steer exploration across the
sample space. Our findings reveal correlations of the electronic properties
unique to surface terminations, local defect density, and point defects.
