  Essentials of the scientific discovery process have remained largely
unchanged for centuries: systematic human observation of natural phenomena is
used to form hypotheses that, when validated through experimentation, are
generalized into established scientific theory. Today, however, we face major
challenges because automated instrumentation and large-scale data acquisition
are generating data sets of such volume and complexity as to defy human
analysis. Radically different scientific approaches are needed, with machine
learning (ML) showing great promise, not least for materials science research.
Hence, given recent advances in ML analysis of synthetic data representing
electronic quantum matter (EQM), the next challenge is for ML to engage
equivalently with experimental data. For example, atomic-scale visualization of
EQM yields arrays of complex electronic structure images, that frequently elude
effective analyses. Here we report development and training of an array of
artificial neural networks (ANN) designed to recognize different types of
hypothesized order hidden in EQM image-arrays. These ANNs are used to analyze
an experimentally-derived EQM image archive from carrier-doped cuprate Mott
insulators. Throughout these noisy and complex data, the ANNs discover the
existence of a lattice-commensurate, four-unit-cell periodic,
translational-symmetry-breaking EQM state. Further, the ANNs find these
phenomena to be unidirectional, revealing a coincident nematic EQM state.
Strong-coupling theories of electronic liquid crystals are congruent with all
these observations.
