Classification of local chemical environments from x-ray absorption spectra using supervised machine learning

X-ray absorption spectroscopy is a premier element-specific technique for materials characterization. Specifically, the x-ray absorption near-edge structure (XANES) encodes important information about the local chemical environment of an absorbing atom, including coordination number, symmetry, and oxidation state. Interpreting XANES spectra is a key step towards understanding the structural and electronic properties of materials, and as such, extracting structural and electronic descriptors from XANES spectra is akin to solving a challenging inverse problem. Existing methods rely on empirical fingerprints, which are often qualitative or semiquantitative and not transferable. In this paper, we present a machine learning-based approach, which is capable of classifying the local coordination environments of the absorbing atom from simulated $K$-edge XANES spectra. The machine learning classifiers can learn important spectral features in a broad energy range without human bias and once trained, can make predictions on the fly. The robustness and fidelity of the machine learning method are demonstrated by an average 86% accuracy across the wide chemical space of oxides in eight $3d$ transition-metal families. We found that spectral features beyond the preedge region play an important role in the local structure classification problem especially for the late $3d$ transition-metal elements.

Figure 1

Workflow of the spectrum-based local chemical environment classification framework using supervised machine learning, which contains three modules: (I) data acquisition supplemented by high throughput computing (HTC) calculations, (II) labeling, and (III) training of machine learning models. The machine learning architecture (set of hyperparameters) used in this paper is shown in Module III. Notably, the model consists of an optional convolutional layer (shown in orange) followed by three hidden layers $l_1,l_2$, and $l_3$ consisting of 90, 60, and 20 neurons, respectively, ending with a softmax output. Further details of the network are described in Sec. 2c.

Figure 2

feff $K$-edge XANES database of eight $3d$ transition-metal families. Spectra were spline interpolated onto discretized grids of 100 points and scaled on the vertical axis such that the maximum value is 1 (prior to shifting the mean to 0 and scaling to unit variance). The intensity of the colors scales inversely with the number of entries per class to aid visualization. Principal component analysis of two regions is shown in the two insets: the full feature space (lower right), and only the preedge region (lower center, discussed in Sec. 3). The $x$ and $y$ axes correspond to the first and second principal axes. The cutoff for the preedge region is delineated by the vertical dashed line. Classes are color coded as follows: blue for tetrahedral ($T4$), green for square pyramidal ($S5$), and red for octahedral ($O6$).

Figure 3

Classwise $F_1$ scores calculated using different machine learning models (CNN/MLP) for $T4$ (blue/cyan), $S5$ (green/light green), and $O6$ (red/pink) local coordination environments in eight $3d$ transition-metal elements. The full height of each bar represents the results trained on the full feature space, while the gray bars overlaid on top with lower-$F_1$ values represent the results for the models trained only on the preedge region. For example, for the Co $S5$ CNN, the $F_1$ score reported for training on the full spectral space is about 0.7 but decreases sharply to about 0.2 when trained on the preedge region only. Error bars correspond to standard deviation; the ones with wider caps correspond to the full feature space.

Figure 4

Comparison between representative experimental (solid) and feff (dashed) XANES spectra. feff calculations are shifted on the energy axis to maximize the Pearson correlation coefficient (PCC) in order to find the best match between experimental and theoretical XANES. The experimental spectra of ${\mathrm{K}}_6{\mathrm{Ti}}_2{\mathrm{O}}_7$ and rutile were extracted from Farges et al. [21], and the experimental spectra of both pairs of Mn and Co oxides were extracted from Manceau et al. [69].

Figure 5

${\overline{F}}_1$ score as a function of the amount of energy shift ($\mathrm{\Delta }E$) applied to the test set. The two graphs on the left illustrate the results of MLCs trained on augmented data (as presented thus far: $\pm 1$ and 2 eV, generating five times the base amount of training data), whereas those on the right illustrate MLCs trained without augmenting the training set.

Figure 6

${\overline{F}}_1$ score as a function of the standard deviation ($\sigma$) used to generate Gaussian random noise, introduced into every point $E$ in the spectra $\mu \left(E\right)$. The two graphs on the left illustrate the results of MLCs trained on a training set augmented with Gaussian random noise of $\sigma =0.03$ (also generating five times the base amount of training data), and those on the right illustrate MLCs trained without data augmentation.