Decoding Structure-Spectrum Relationships in X-Ray Absorption Spectra with Physically Organized Latent Spaces

X-ray absorption spectroscopy (XAS) is a premier materials characterization technique, which is element specific and sensitive to the local chemical environment. However, the physical information in XAS, in particular, x-ray absorption near-edge structure (XANES), is encoded in the spectral function in an abstract form. First principles calculations are widely used to unravel the complex structure-spectrum relationship. However, this approach requires a great deal of domain expertise and is computational expensive. These drawbacks limit the scope of XAS modeling for complex systems and in real-time analysis. To address this challenge, data-driven XAS analysis methods emerge, which take advantage of the fast developing machine learning tools for spectral interpretation. Successful examples show that machine learning models can be used to accelerate XAS simulations and identify the physical origin of spectral trends in a statistically salient way.<br/><br/>In this study, a semi-supervised machine learning method for the discovery of structure-spectrum relationships is developed and then demonstrated using the specific example of interpreting XANES spectra. This method constructs a one-to-one mapping between individual structure descriptors and spectral trends. Specifically, an adversarial autoencoder is augmented with a rank constraint (RankAAE). The RankAAE methodology produces a continuous and interpretable latent space, where each dimension can track an individual structure descriptor. As a part of this process, the model provides a robust and quantitative measure of the structure-spectrum relationship by decoupling intertwined spectral contributions from multiple structural characteristics. This makes it ideal for spectral interpretation and the discovery of descriptors. The capability of this procedure is showcased by considering five local structure descriptors and a database of more than 50000 simulated XANES spectra across eight first-row transition metal oxide families. The resulting structure-spectrum relationships not only reproduce known trends in the literature but also reveal unintuitive ones that are visually indiscernible in large datasets. The results suggest that the RankAAE methodology has great potential to assist researchers in interpreting complex scientific data, testing physical hypotheses, and revealing patterns that extend scientific insight.