  Topological materials discovery has emerged as an important frontier in
condensed matter physics. While theoretical classification frameworks have been
used to identify thousands of candidate topological materials, experimental
determination of materials' topology often poses significant technical
challenges. X-ray absorption spectroscopy (XAS) is a widely-used materials
characterization technique sensitive to atoms' local symmetry and chemical
bonding, which are intimately linked to band topology by the theory of
topological quantum chemistry (TQC). Moreover, as a local structural probe, XAS
is known to have high quantitative agreement between experiment and
calculation, suggesting that insights from computational spectra can
effectively inform experiments. In this work, we leverage computed X-ray
absorption near-edge structure (XANES) spectra of more than 10,000 inorganic
materials to train a neural network (NN) classifier that predicts topological
class directly from XANES signatures, achieving F$_1$ scores of 89% and 93% for
topological and trivial classes, respectively. Additionally, we obtain
consistent classifications using corresponding experimental and computational
XANES spectra for a small number of measured compounds. Given the simplicity of
the XAS setup and its compatibility with multimodal sample environments, the
proposed machine learning-augmented XAS topological indicator has the potential
to discover broader categories of topological materials, such as non-cleavable
compounds and amorphous materials, and may further inform field-driven
phenomena in situ, such as magnetic field-driven topological phase transitions.
