Prediction of the Cu Oxidation State from EELS and XAS Spectra Using Supervised Machine Learning

Our RF model shows a high level of accuracy on a test set of simulated data. Figure 2a shows the $R^{2}$ plot of the predictions of this test set, which contains roughly 2400 spectra. The $R^{2}$ for this model is 0.85, and shows a visible high degree of correlation across all the well represented oxidation states. The largest errors come from integer valence misprediction, most commonly when a Cu(0) or Cu(I) spectrum is predicted as mixed valence. However, as shown in Figure 2a, these mispredictions can often be differentiated from the accurate predictions by using the prediction standard deviation (described in the methods section). The feature importance plot from Figure 2c offers insights into the origin of these errors. The model takes a small amount of information from the pre-edge and then bases its prediction mostly on the location and shape of the L₃ peak. As Cu(0) and Cu(I) have L₃ peaks at almost exactly the same energy, these are harder to differentiate than Cu(II), which is red shifted by roughly 3 eV. Despite this difficulty, Cu(0) and Cu(I) are accurately identified far more often than they are mispredicted, as shown in Figure 2a. As can be seen from Figure 2b, a full integer miss, i.e. a Cu(0) spectrum incorrectly called a Cu(I) spectrum, essentially never occurs. What is even more encouraging in Figure 2a and 2b is the simulated mixture samples are frequently predicted with a high degree of accuracy, showing this model has significant potential in predicting mixed valence samples.

In this work we have developed a method for quantifying the uncertainty in our RF model’s prediction. This is done by examining the predictions of each of the 500 decision trees which comprise the random forest as well as the averaged value used as the final prediction. This uncertainty analysis is visualized by generating a prediction histogram, as shown in Figure 1 (IV) and Figure 3d-3f. Beyond the qualitative spread of predictions shown in the prediction histograms, the uncertainty can be understood quantitatively by calculating the standard deviation of these predictions. This is indicated by the horizontal green line in the prediction histogram plots shown in Figures 1 and 3, and is used here as the RF model’s internal uncertainty measurement. To leverage this quantitative uncertainty, the standard deviation can be used to filter out predictions that are highly uncertain, and therefore presumably less accurate. Figure LABEL:std_threshold illustrates this concept, where a standard deviation threshold was imposed, and all predictions with a standard deviation higher than this value were discarded due to their high uncertainty. The standard deviation can be used as a powerful tool in determining significantly inaccurate predictions on simulated data, as can be seen when the threshold is set at 0.35 (red rectangle in Figure LABEL:std_thresholda and LABEL:std_thresholdb). When this threshold is used, 15% of the predictions of our test set are higher than the threshold and discarded (Figure LABEL:std_thresholda). However, imposing this threshold causes the RMSE of the remaining 85% of our test set to decrease 8% from the full test set value of 0.24 to 0.22 (Figure LABEL:std_thresholdb). Therefore, the 15% of the test set discarded by this method is comprised of predictions less accurate than average, showcasing the utility of this uncertainty metric in informing the accuracy of the model’s predictions for unknown samples.

To test the RF model’s validity when applied to experiments, we used the model to predict a set of metallic Cu and Cu oxide standards. The simulated spectra corresponding to these standards were left out of both the training and test sets previously discussed. These standards were smoothed using a Savitzy-Golay filter with a window size of 1.5 eV and a polynomial order of 3. From Figure LABEL:smoothing_impact it can be seen that the level of smoothing does not impact prediction accuracy. The smoothing window of 1.5 eV was selected as the default method due to qualitative observations that it removed the vast majority of the noise but also preserved the overall shape of the spectrum (Figure LABEL:model_outline). From Figure 3e and 3f it can be seen that the model has a high degree of accuracy when predicting Cu(I) and Cu(II), rendering essentially perfect predictions for each of these standards, regardless of whether the mean or the median of the decision tree ensemble is used as the prediction. However, Figure 3d shows the Cu(0) standard appears to be slightly over estimated, with the mean prediction rendering a larger overestimate than the median, as the two predict 0.3 and 0.05, respectively.

There are likely two factors responsible for the overprediction of Cu valence for metallic absorbers. First, as has been discussed above, random forest models average predictions across individual decision trees, in this case 500. Therefore, it will always be more challenging for this model to predict Cu(0) as exactly zero, as all Cu atoms in our training data have non-negative valence. Consequently, any spread in the predictions will result in an overestimate. It is also worth noting that Figure 3d shows that the mode of our prediction histogram contains Cu(0) by a factor of four over the next highest bar, and that the median is much closer to a prediction of Cu(0). A second factor may also partially explain this overestimate, which is that our Cu(0) likely experienced some surface oxidation. Therefore, it may be assumed that this material no longer had a true oxidation state of zero at the time of measurement. This is reflected in the spectrum, which can be seen to have visibly taken on some additional Cu(I) character relative to simulated Cu(0) and Cu(0) observed in XAS studies taken from the literature (Figure LABEL:xas_vs_eels, [21]). Specifically, our Cu(0) spectrum shows a drop in intensity of the two higher energy peaks in the L₃ edge and an increase in intensity in the lowest energy peak, which are characteristic of surface oxidation leading to more visible Cu(I) character. This, combined with the logistics surrounding the attainment of our Cu(0) sample, the sample was not shipped in vacuum sealed vial, and the fact that we were unable to reduce the sample in the microscope, supports the supposition that our Cu(0) EELS sample has undergone some surface oxidation. Therefore, we believe that this prediction of a mixed valence material closer to Cu(0) than Cu(I) matches our experimental realities and a detailed examination of the experimental spectrum.

However, it is also important to note that an XAS spectrum of Cu(0) extracted from the literature (Figure 4d) is also overestimated by our model. This is unlikely to be a result of surface oxidation, both from an instrumental perspective and a qualitative examination of the spectrum, which shows a much more characteristic Cu(0) sample than our experimental EELS sample due to the relatively equal heights of the three L₃ edge peaks and the L₃ being lower in intensity than the L₂ edge (Figure LABEL:feff_to_lit, S7). We attribute the overestimation of the literature Cu(0) mainly to the fact that our model does not allow for non-positive predictions, which causes any uncertainty in the prediction of Cu(0) to result in an overestimate, as discussed above.

In addition to the experimental spectra predicted here and in the following section, 8 other spectra extracted from the literature were predicted using this model (Figure LABEL:other_exp_samples, LABEL:shift_other_exp_samples)[47, 48, 49]. 7 of these 8 spectra were materials with a Cu(I) oxidation state and all are predicted to within 0.1 of Cu(I) when the edge alignment is correct, and most retain their accuracy when the edge is misaligned by 0.5 eV in either direction (Figure LABEL:shift_other_exp_samples). The one Cu(II) material, CuS, is predicted as roughly 1.5, however, our model’s prediction is likely inaccurate due to this spectrum’s high intensity post the L₃ region (Figure LABEL:CuS). As the Cu(II) L₃ edge is roughly 2eV lower in energy than Cu(I) and Cu(0), this increased intensity is likely mimicking a mixed valent spectrum, with this extra intensity appearing to come from absorption from a Cu(I) material. XAS is impacted by multiple photon scattering in very thick samples, which produces artificially high intensity in the tail of the L_2,3 edge spectrum. Therefore, we believe that this was simply a spectrum of a very thick sample, leading to multiple scattering induced changes to the spectrum that the model is unable to account for.

Given that we have performed a manual edge alignment correction to our training data, we also examine the impact of energy axis misalignment on our predictions of experimental spectra. To explore this, we created a set of experimental spectra where the onset energy was shifted by controlled amounts and tracked how this shift impacted the oxidation state prediction (Figure 4). From Figure 4a we see that the energy misalignment has the greatest impact on the Cu(0) sample, and an offset of -0.4 eV or greatercauses an inflection point where the prediction jumps from 0.3 to nearly 0.5. Misalignment in the positive direction has a far less dramatic impact, and an energy shift of +0.5 eV produces essentially no change in the prediction. The Cu(I) sample, shown in Figure 4b, is more stable, with a shift of nearly 1 eV in either direction resulting in a change of less than 0.2 in the oxidation state prediction. In Figure 4c, we see that Cu(II)’s prediction is virtually independent of shift plus/minus 1 eV, which is likely explained by the greater than 2 eV gap between the onset energy of Cu(II) vs Cu(I) and Cu(0).

To further examine the utility of our model when applied to experimental spectra, and to further study the impact of absolute energy shift, an additional experimental validation was done using an extracted set of XAS spectra of Cu oxides [21]. This set of spectra has been measured to be shifted from the experimental spectra used to validate this model by -1.0 eV for the Cu metal spectrum and -1.2 eV for the Cu₂O and CuO spectra (Figure LABEL:feff_to_lit), and provides a test case for how the model will respond to spectra with their energy axes significantly misaligned. From Figure 4d-f, we can see that our ML model produces excellent results for the XAS spectra when they are correctly aligned to our training data (red line in Figure 4d-f) and the results are robust even when the raw spectra are predicted, which are severely misaligned (black line in Figure 4d-f). When such a misalignment has occurred, the Cu(I) and Cu(II) spectra are predicted with near perfect accuracy, while the Cu(0) spectrum appears to be slightly over estimated, returning a prediction of around 0.5 when the correct alignment prediction is 0.28. It is worth reflecting this prediction is still an overestimate, although closer to zero than our experimental EELS spectrum shown in Figure 3d, reflecting this model’s propensity to overestimate Cu(0). With these observations, it is clear that the ML model trained on properly aligned spectra can achieve highly accurate results on spectra with significant energy misalignment. Additionally, a potential avenue to determine the true alignment location is to vary the energy axis and seek out regions of consistent stability and low prediction standard deviation, as these regions are often associated with more accurate predictions for our experimental data.

Post successful proof of concept for our model on standard experimental samples, we turn our attention to a more valuable, but also more challenging, experimental case, the prediction of samples of mixtures of different oxidation states. As shown in Figure 2a, our model has already demonstrated a high degree of accuracy on simulated mixed valence samples. Additionally, we show how smooth variance in simulated mixed valence materials excluded from the training data is captured by our model by showing simulated mixtures of Cu(0), Cu(I) and Cu(II) in Figure LABEL:simulated_mixtures. The important test for the utility of this model in experimental spectra is how well this process works on experimental mixtures of oxidation states. Due to the difficulty in engineering a system with smoothly varying mixed valence states, and inherent uncertainties in quantifying such a system, we have generated mixed valence experimental spectra through linear combinations of our standard samples. The labeled value for these experimental mixtures is determined by multiplying their formal oxidation state by their contribution to the final mixture spectrum, as was done with the labeling for the simulated mixtures. For example, a mixture of 40% Cu(0) standard and 60% Cu₂O standard would be calculated as follows:

The results are shown in Figure 5. From Figure 5a-b, we see both plots contain regions of high accuracy, particularly for mixtures of Cu(I) and Cu(II) (Figure 5b). These mixtures are accurately predicted to within less than 0.1 in close to half of the mixture samples. However, we can see that the absolute accuracy has sections of low accuracy, particularly at inflection points where the prediction is changing quickly. This is particularly true for mixtures of Cu(0) and Cu(I) (Figure 5a), where the inflection region drives the prediction into a region of significant overestimation which is not recovered until the mixture becomes entirely Cu(I). However, the overall trend of the prediction is correct, as in both Figure 5a and b the higher valence sample is identified as such until a pure sample is predicted, regardless of any absolute inaccuracies in the prediction.

Both mixed valence cases tend overestimate the oxidation state when the higher oxidation state sample comprises greater than 50% of the mixture. We believe this to be a feature of the higher maximum intensity and sharper peaks of higher oxidation state spectra. This can be seen in Figure 3a-c, where the edge intensity relative to the tail of each spectrum is shown. This is also noticeable in the cumulative spectrum, which is the actual input into the model, (inset in Figure 3a-c) where the lower intensity in the Cu(0) peak results in an almost linear cumulative spectrum, while the higher intensity of Cu(I) and Cu(II) are very noticeable as a sharply increasing region in the L₃ edge region of the cumulative spectrum. The higher intensity of the higher oxidation state may make the fine features of Cu(0) difficult to detect at low mixture fractions, as Cu₂O and Cu(0) have their onset edges and L₃ peaks at essentially the same energy. Additionally, The slight red shift in Cu(II) spectra yields an immediately noticeable feature for model identification, and a sample which is 75% Cu(II) and 25% Cu(I) may simply be predicted as a Cu(II) with a shoulder or other unusual transition, which is relatively common in the simulated data.

We have also predicted random experimental mixtures of Cu(0), Cu₂O, and CuO. This was done using mixtures of the literature XAS spectra and our experimental EELS data. The results are shown in Figure LABEL:empirical_correctiona and c, respectively. They contain a characteristic overestimation as seen in the smoothly varying mixed valent binary mixtures, which inspired the creation of an empirical correction to random mixed valent spectra. The literature XAS predictions were used to train a linear regression model to predict the true oxidation state based on the prediction of the unknown spectrum. This was done using the mean, median and standard deviation of the decision trees as input. The model was trained and validated using the random mixtures of the literature XAS data and tested on the predictions of the random mixtures of EELS data. Figure LABEL:empirical_correctiona-b shows the predictions on the training data, the literature XAS sample, and how the empirical correction improves the predictions. Upon generation of this empirical model, it was used to correct the predictions of mixtures of Cu(0), Cu₂O, and CuO experimental EELS spectra. The results of applying this correction are shown in Figure LABEL:empirical_correctionc-d. The generation of this empirical model shows that, despite the challenges of predicting a pure Cu(II) in the empirical model’s predictions, the overall trend of the mixed valent overestimation can be captured and corrected.

As Figure 3d clearly shows that the median/mode of the decision trees yields a prediction much closer to Cu(0) for our experimental EELS Cu(0) sample, and Figure 5 shows a characteristic overestimation in both types of experimental mixtures, it is worth exploring whether using the median or the mode as a prediction, rather than the mean, is more accurate overall. This idea is explored in detail in Figure LABEL:mean_median_and_mode, which shows the full prediction histogram for various mixtures of Cu(0) and Cu₂O (Figure LABEL:mean_median_and_modea-f) and compares the median, mean and mode predictions directly (Figure LABEL:mean_median_and_modeg-i). From Figure LABEL:mean_median_and_mode we see that, although the median is more accurate for pure Cu(0), it quickly begins to overestimate the oxidation state by a margin significantly greater than the prediction using the mean of the decision trees. The mode prediction is even more extreme, jumping from predicting Cu(0) for pure Cu(0) and 80/20 mixtures of Cu(0) and Cu₂O, to a prediction of Cu(I) for 60/40 mixtures of Cu(0) and Cu₂O. Therefore, for predictions of mixtures of oxidation states, the mean prediction is more likely to be accurate, and mean/mode statistics can be helpful in instances where a pure oxidation state is assumed, particularly if the material is expected to be metallic. Due to this utility, predictions using this model return the full set of predictions as well as the mode, median and the mean of the decision trees.

To test the impact of noise on the simulated data, random Poisson noise was added to each simulated spectrum in the test set to produce a test set augmented by noise. To ensure that this process echoed our approach on experimental spectra as much as possible, the simulated spectra, which are on a 0.1 eV resolution, were re-sampled using scipy’s 1d interpolation function with a higher resolution of 0.03 eV, matching that of our experimental samples. Noise was then added to the interpolated spectra, and these spectra were then smoothed in the same method as the experimental spectra and integrated to produce a cumulative spectrum (Figure LABEL:model_outline). These spectra were then predicted by the model to test its accuracy on noisy data.

As shown in Figure 6a, the simulated data are relatively sensitive to noise augmentation, and the addition of a small amount of Poisson noise resulted in an increase in RMSE from 0.24 to 0.3 as compared to results from the noiseless spectra. Further increase in noise led to an even larger RMSE, however the decline in accuracy becomes less sharp than the initial slope. A similar trend is seen in Figure 6b for $R^{2}$, where a drop in $R^{2}$ is observed after adding a small amount of noise, however this decline is less sharp than the increase in RMSE, and adding additional noise has a more pronounced decline on $R^{2}$ than subsequent noise does on RMSE. Despite this observation, the noise level of our experimental spectra, which are noticeably larger than the simulated low noise case, do not appear to suffer as much as these simulated noisy spectra (Figure LABEL:model_outline). An examination of the quantitative noise level of the experimental spectra can be found in Figure LABEL:quantify_noise, which shows that the noise STD for the experimental EELS spectra is between 0.03 and 0.05. Additionally, the selection of the random seed for the addition of noise appears to have a significant impact on the overall accuracy of the noisy test set. This is shown with the error bars in Figure 6a and 6b, which represent the standard deviation across 100 different random noise seed states. The presented RMSEs and $R^{2}$s are the average values across these 100 random states. A detailed examination of the noise profiles for these higher error random states shows that in these spectra the region around the baseline experiences noise spikes that mimic features around the baseline region, similar to how an inaccurate power law subtraction of an EELS spectrum baseline appears. This observation further enforces that the accuracy of this model relies heavily on the accurate identification and subtraction of the baseline.

In this work, simulated FEFF9 XAS spectra of Cu materials were extracted from the Materials Project. This initial extraction produced a dataset of site averaged spectra for 1533 materials, which contains the 59 materials shown in Figure 1I labeled as neither predicted stable nor synthesized [40]. To increase the volume of our training data, an additional 2000 structures were selected by searching the Materials Project for all Cu containing materials that had either been previously synthesized or were predicted to be stable by theory [39]. This choice screens a broad material space that is likely accessible to experiments. We computed 2000 site averaged spectra using the Lightshow workflow [50] and FEFF9 [46]. The combination of this augmentation step and the initial extraction of L-edge spectra already generated by the Materials Project provided 1199 materials that both have been experimentally synthesized and are predicted to be stable (Figure 1I). For each structure, unique Cu sites are determined by the space group symmetry. Then site specific spectra were calculated using FEFF9. The L₂ and L₃ spectra for each site were combined into the L₂,₃ spectrum by summing the L₂ and L₃ spectra, after first interpolating onto the same energy grid (Figure LABEL:L2_3). The site averaged spectrum is calculated from the weighted sum of site-specific spectra based on the multiplicity of the unique sites in the unit cell. The oxidation state of the site averaged spectra spectra were determined using the Materials Project’s “average oxidation states” function [39]. Despite this averaging procedure, greater than 93% of the site averaged spectra retained integer valence. When FEFF9 failed to converge for some, but not all, of the sites in a material, converged site spectra were averaged leaving out the failed spectra.

To prepare our training set of 3500 site averaged spectra, several additional steps were performed. This workflow is summarized in Figure 1. First, spectra were interpolated to ensure they were all on a 0.1 eV energy resolution. Second, the non uniformity in the energy range of the L₃ edge, specifically at the starting point, was addressed by fitting a 6th order polynomial to connect the lowest energy point to [925, 0] (i.e., vanishing intensity at 925 eV) for every spectrum (see Figure LABEL:baseline). The spectra were then aligned to ensure their onset edges were in the same general energy range as those seen in experimental EELS Cu materials, as it was observed that FEFF9 was producing a systematic misalignment in the absolute energy of the L_2,3 edge .

To accomplish this alignment, two systematic errors were corrected. First, a high degree of onset energy variability was observed across zero valence materials, which would be expected to all have similar onset energies. Second, the absolute energy of the simulated spectra were several eV off from experimental standards. Both of these issues were fixed simultaneously by our automated alignment procedure. Below is a brief summary of our edge alignment procedure following the $\Delta$SCF method [51, 52], as shown in equation (2):

where $E_{raw}$ and $E_{align}$ are the excitation energies before and after alignment. In order to correct the inaccuracy in the calculated excitation energy, we scale the raw spectrum by the difference between the Fermi energy ($\epsilon_{Fermi}$) and Cu 2p core level ($\epsilon_{Core}$) and by the total energy difference between the core-hole excited state ($\epsilon_{XCH}$) and the ground state ($\epsilon_{GS}$). In the core-hole excited state, the core electron is placed at the bottom of the conduction band, known as the excited core-hole (XCH) method. After this alignment, there is a single empirical constant ($\Delta$) calibrated on a reference system to account for the residual discrepancy between theory and experiment. In our study, $\epsilon_{Fermi}$ is taken from the FEFF9 output corresponding to k=0, where k is the photoelectron wave number. $\epsilon_{Core}$ is set to -916.8226 eV, which is determined by the VASP estimation of the energy of a 2p core hole in Cu[52, 53]. ($\epsilon_{XCH}$ - $\epsilon_{GS}$) was computed using the VASP code base, and the values are -650.888 eV, -650.748 eV and -651.945 eV for Cu, Cu₂O and CuO, respectively [53]. In principle, one should perform VASP calculations for all the systems in the database. However, this will lead to a very high computational cost, which is impractical for the scope of this study. Therefore, we treated ($\epsilon_{XCH}$ - $\epsilon_{GS}$) as constant for each oxidation state, using the Cu, Cu₂O and CuO values listed above for Cu(0), Cu(I) and Cu(II) spectra respectively. This resulted in a simplification of equation (2), where ($\epsilon_{XCH}$ - $\epsilon_{GS}$) + $\Delta$ is treated as a constant, $\delta_{ox}$, with different values for each oxidation state. These are: 1849.06 eV, 1849.33eV and 1846.87 eV for Cu with oxidation state of 0, +1 and +2, respectively, which aligns simulated Cu, Cu₂O and CuO spectra to their corresponding EELS experimental spectrum. For the small subset of materials that were classified as mixed valence, they were aligned based on whichever integer oxidation state they were closest to.

It is important to note that this alignment procedure is not aligning the edge to the exact location of the Cu/ Cu₂O/CuO edges for all Cu 0, +1 and +2 spectra (i.e. forcing every Cu(II) spectrum to start at 930.2 eV, where the CuO edge is located). This alignment procedure computes a correction based on FEFF9’s Fermi energy prediction and then uses the energy gap between the simulated spectrum of either Cu metal, Cu₂O and CuO, post Fermi correction, and the corresponding experimental spectrum to scale all spectra with that oxidation state. For example, not every Cu(II) spectrum is at the same edge energy, and many of them are quite different based on their initial location post Fermi energy correction. The relative energy alignment from FEFF9 within an oxidation state is often preserved, particularly for Cu(I) and Cu(II) materials, and this scaling using the experimental spectra is done to bring the energy axis to experimental relevance. Without this correction, the energy axis for the FEFF9 spectra is misaligned by multiple eV and any experimental prediction is impossible. An example of this alignment procedure is shown in Figure LABEL:energy_alignment.

Our spectral dataset was then augmented by generating simulated mixed valence samples (see step III in Figure 1, Figure LABEL:mixture_generation). To accomplish this, 300 random sets of spectra were drawn from the integer dataset, each draw taking a random Cu(0), Cu(I) and Cu(II) site averaged spectrum. Each of these 300 sets of 3 integer spectra were then linearly combined to mimic mixed valence structures. For each set of three spectra, 20 random fractions of each material were combined to produce a simulated mixed valence spectrum. To ensure an even spread of mixed valences, 100 sets were combinations of Cu(0) and Cu(I), 100 were combinations of Cu(I) and Cu(II), and 100 were combinations of Cu(0), Cu(I) and Cu(II). This mixture produced a final dataset of roughly 9500 spectra with data well distributed from Cu(0) to Cu(II) (step III in Figure 1, Figure LABEL:mixture_generation). Our training and test sets were generated by separating classes of mixtures, rather than a random 75/25 split across the full 9500 spectra dataset. To accomplish this, we tracked the compositions of each random mixture, and ensured each composition was fully placed in either the training or test set. For example, an arbitrary mixture of Cu(0), Cu(I) and Cu(II) would have 20 random proportions of each material in our full dataset, and our train/test split ensured all 20 of these were either in training or test. This ensures the model is not biased by seeing a 0.3 0.3 0.4 mixture of the above materials in training and then tested on a mixture of 0.2 0.3 0.5 of the above compounds, which results in a very similar spectrum.

To achieve the best ML model performance, we have tested different spectral representations, including the spectrum itself, its first and second derivative, and the cumulative integral of the spectrum. We found that the best model performance was achieved with the cumulative integral with intensity normalized to 1. In addition, using the cumulative integral, referred to as a cumulative spectrum in this work, as input feature can ensure consistency in the absolute scale of the EELS spectrum. This representation can simplify intensity scaling, as experimental post processing decisions and noise can create a high degree of variability in spectral intensity. The cumulative spectrum approach is insensitive to the absolute scale of the spectrum, although it does require an accurate identification and subtraction of the baseline for experimental spectra.

Random forest (RF) models for this work were trained using Scikit-learn’s RandomForestRegressor model [54]. The number of trees was fixed at 500, with all features available and max depth unfixed. The dataset was split into train and test components using a 75/25 random train test split function from Scikit-learn. The structure of this model allows for the input of a raw spectrum of arbitrary min and max energy and energy scale. The model then takes the input spectrum and interpolates it to a 0.1 eV resolution from 925 to 970 eV to ensure the consistency of the energy grid used in the training data. Spectral smoothing is then applied using a Savitzy-Golay filter from scipy [55]. The smoothing step is done before the interpolation provided that the inputted spectrum is on an evenly spaced energy scale. The cumulative operation on the spectrum is then performed and this spectrum is the input of the model. The trained RF model is an ensemble of 500 individually trained decision trees, and returns the predictions of each decision tree. A simple average of inferred valence values from each tree is taken as the final prediction, although median and mode predictions can be returned as well. The mode prediction is determined by finding the highest count on a histogram with bin widths of 0.2. The mode is determined by finding the center of the highest bin, meaning integer valence predictions will be returned as 0.1 higher than the integer valence (ie a prediction of Cu(0) will have a mode of 0.1 assigned to it, as the bin will range from 0.0 to 0.2). The standard deviation of these 500 predictions can approximate the model’s internal confidence in its prediction, and is visualized in the prediction histogram in Figures 1, 3 and LABEL:model_outline, the last of which illustrates the entirety of the processing steps performed on an input spectrum.

To validate the utility of this model on experimental data, experimental EELS spectra of standard reference samples were measured, including Cu metal, Cu₂O and CuO. Cu metal was purchased from Sigma-Aldrich with 99.999% purity. Cu₂O and CuO were purchased from Sigma-Aldrich with 99.99% purity. The Cu₂O sample was measured using a vacuum holder to prevent oxidation. However, the Cu metal sample was not delivered in a vacuum sealed container, and under the assumption that surface oxidation had already occurred, a vacuum holder was not used for this sample. Using the TEAM I microscope, a double-corrected Thermo Fisher Titan microscope, we acquired monochromated reference data for these samples at roughly 0.2 meV resolution. Data were collected at 300kV with a semi-convergence angle of 17 mrad and a collection angle of 82 mrad. All data was collected using a Gatan Continuum spectrometer equipped with a K3-IS detector operated in electron counting mode. Spectra were baseline subtracted using the GMS Digital Micrograph software package, and spectra were taken using dual EELS to dynamically remove shifts in the reference elastic energy and deconvolved with the simultaneously measured zero-loss region to mitigate artifacts from electrons experiencing multiple scattering events. The deconvolution of multiple scattering is essential to ensure the experimental EELS spectra are comparable to XAS.