Interpretable Multimodal Machine Learning Analysis of X-ray Absorption Near-Edge Spectra and Pair Distribution Functions

TL;DR

This work demonstrates that interpretable random-forest models can fuse XANES and PDF data to characterize local environments around transition-metal cations in oxides. Across four metals (Ti, Mn, Fe, Cu), XANES generally provides stronger, site-specific structural information than total PDFs, while differential PDFs offer complementary signals that enhance certain predictions. Multimodal models often yield modest improvements, with notable gains when using dPDFs, especially for bond-length estimation and Fe-related predictions, highlighting the value of species-specific signals. The results provide actionable guidance for experimental design and data fusion strategies, illustrating when combining XANES and PDF modalities adds meaningful information to structural investigations.

Abstract

We used interpretable machine learning to combine information from multiple heterogeneous spectra: X-ray absorption near-edge spectra (XANES) and atomic pair distribution functions (PDFs) to extract local structural and chemical environments of transition metal cations in oxides. Random forest models were trained on simulated XANES, PDF, and both combined to extract oxidation state, coordination number, and mean nearest-neighbor bond length. XANES-only models generally outperformed PDF-only models, even for structural tasks, although using the metal's differential PDFs (dPDFs) instead of total PDFs narrowed this gap. When combined with PDFs, information from XANES often dominates the prediction. Our results demonstrate that XANES contain rich structural information and highlight the utility of species-specificity. This interpretable, multimodal approach is quick to implement with suitable databases and offers valuable insights into the relative strengths of different modalities, guiding researchers in experiment design and identifying when combining complementary techniques adds meaningful information to a scientific investigation.

Figures (21)

• Figure 1: Oxidation state classification results: (a) test F1 scores for XANES (left bar of each triplet, no pattern), PDF (middle bar with circular pattern), and XANES+PDF models (right bar with striped pattern). Results are shown for the four datasets, from left to right: Ti (orange), Mn (green), Fe (blue), and Cu (magenta). Black horizontal lines indicate F1 scores from a trivial classifier that labels all samples as the modal class. Error bars on the test scores represent one standard deviation. Feature importance plots are shown for (b) Ti and (c) Fe datasets, for (i) XANES features, (ii) PDF features, and (iii) XANES+PDF features. In (i) and (ii), the XANES and PDF spectra are plotted in light gray, with scales defined by the secondary $y-$axis on the right. The dark gray line represents the average spectrum. Vertical dotted lines mark the locations of prominent features from the XANES- and PDF-only importance plots. To highlight changes in feature importance for the combined XANES+PDF models, the same lines are shown in (iii) for comparison.
• Figure 2: Coordination number classification results: (a) test F1 scores for XANES (left bar of each triplet, no pattern), PDF (middle bar with circular pattern), and XANES+PDF models (right bar with striped pattern). Results are shown for the four datasets, from left to right: Ti (orange), Mn (green), Fe (blue), and Cu (magenta). Black horizontal lines indicate F1 scores from a trivial classifier that labels all samples as the modal class. Error bars on the test scores represent one standard deviation. Feature importance plots are shown for (b) Ti and (c) Fe datasets, for (i) XANES features, (ii) PDF features, and (iii) XANES+PDF features. In (i) and (ii), the XANES and PDF spectra are plotted in light gray, with scales defined by the secondary $y-$axis on the right. The dark gray line represents the average spectrum. Vertical dotted lines mark the locations of prominent features from the XANES- and PDF-only importance plots. To highlight changes in feature importance for the combined XANES+PDF models, the same lines are shown in (iii) for comparison.
• Figure 3: Bond Length Regression Results: (a) test RMSE scores expressed as a percentage of the mean bond length for XANES (left bar of each triplet, no pattern), PDF (middle bar with circular pattern), and XANES+PDF models (right bar with striped pattern). Results are shown for the four datasets, from left to right: Ti (orange), Mn (green), Fe (blue), and Cu (magenta). Note that for these RMSEs smaller numbers indicate better model performance. Error bars on the test scores represent one standard deviation. Feature importance plots are shown for (b) Ti and (c) Fe datasets, for (i) XANES features, (ii) PDF features, and (iii) XANES+PDF features. In (i) and (ii), the XANES and PDF spectra are plotted in light gray, with scales defined by the secondary $y-$axis on the right. The dark gray line represents the average spectrum. Vertical dotted lines mark the locations of prominent features from the XANES- and PDF-only importance plots. To highlight changes in feature importance for the combined XANES+PDF models, the same lines are shown in (iii) for comparison.
• Figure 4: differential-PDF (dPDF) results on Bond Length Regression: (a) test RMSE scores expressed as a percentage of the mean bond length for XANES (left bar of each triplet, light color with no pattern), PDF (middle bar with circular pattern), and dPDF models (right bar, black). Results are shown for the four datasets, from left to right: Ti (orange), Mn (green), Fe (blue), and Cu (magenta). Note that for these RMSEs smaller numbers indicate better model performance. The XANES and PDF results from Fig. \ref{['fig:bl']} are reproduced here for easy comparison. Error bars on the test scores represent one standard deviation. (b) Change in RMSEs when training the models on multimodal inputs, combining XANES with PDF (solid) or dPDF (black, striped). Negative changes in RMSEs (for Mn, Fe, and Cu) indicate an improvement over the XANES-only models. (c) Feature importance plots for the multimodal inputs, comparing XANES+PDF (dashed line) and XANES+dPDF (solid line) models for Fe.
• Figure S1: Histograms of mean nearest-neighbor bond lengths for all four datasets (Ti, Mn, Fe, and Cu).