Chemical Composition-Driven Machine Learning Models for Predicting Ionic Conductivity in Lithium-Containing Oxides

Abstract

A machine learning model that can predict the ionic conductivity of lithium-containing oxides using chemical composition and ionic conductivity data was previously developed. However, this model revealed several limitations, leading to less-than-ideal prediction accuracy. Thus, new models demonstrating improved prediction ability must be developed. This study presents the development of machine learning models for the accurate prediction of ionic conductivity in lithium-containing materials based solely on their chemical composition. The models constructed using the NGBoost and LightGBM algorithms show high compatibility with the training and test data, resulting in high predictive accuracy. The constructed models identify “entropy,” which is considered a key factor in developing ionic conductors, as an important feature. This finding highlights the potential utility of this property from a solid-state chemistry perspective. The developed models demonstrate high predictive accuracy even for previously reported lithium superionic conductor-type materials that were not included in the training dataset. The established models are expected to facilitate efficient material discovery for the development of all-solid-state lithium batteries.

1. Introduction

Lithium-ion conductors are key materials that function as solid electrolytes in all-solid-state lithium batteries. Although various characteristics (e.g., conductivity, chemical stability, electrochemical window, etc.) are required for solid electrolytes, high ionic conductivities of over 10⁻³ S cm⁻¹ are generally desired at practical operating temperatures of approximately 300 K.^1,2 In this context, sulfide-based materials have attracted much attention because of their high ionic conductivity.³ Highly conducting novel solid electrolytes for other systems (e.g., oxides,⁴ halides,^5,6 and hydrides⁷) have been reported in the last decade. Therefore, the search for similar materials should include a broader scope of chemical compositions.

Recent progress in advanced theoretical calculations, simulations, and machine learning approaches has revealed various candidates (e.g., oxides, sulfides) as suitable solid electrolytes (10⁻³ S cm⁻¹) from the existing chemical database and/or simulated virtual materials. However, no cases of new materials proposed by computational chemistry showing the expected crystal structure and ionic conductivity have been reported.^8–10

The chemical composition of most predicted materials is strictly defined because diffusion coefficients and conductivities must be theoretically calculated based on the specified chemical composition and crystal structure. However, classical and powerful material searches consider nonstoichiometric chemical compositions and the regions in which solid solutions of certain crystalline phases are formed. This approach has been used to develop copper and lithium solid electrolytes with the highest conductivity in the phase diagrams of RbCl–CuCl–CuI and Li₂S–GeS₂–P₂S₅, respectively,^11,12 indicating that state-of-the-art machine learning methods should be designed to determine the target region in which highly conducting materials could exist in a phase diagram.

Motivated by these considerations, the authors developed a machine-learning model that can predict the ionic conductivity of lithium-containing oxides using chemical composition and ionic conductivity data.¹³ Regression analysis for this model was conducted using the random forest algorithm, and a dataset containing 256 conductive lithium oxides was used for learning. Statistical processing (e.g., mean, variance, standard deviation) based on chemical composition and element information (e.g., effective ionic radius, electronegativity, polarizability) was performed to generate 820 features that could be used for regression analysis.

The power of this prediction model was examined by comparing the predicted and experimental conductivities in the Li₂O–SiO₂–MO₃ ternary diagram. As shown in Fig. 1a, the tie-line of Li₄SiO₄ and Li₂MoO₄ (Li_4−2xSi_1−xMo_xO₄) was expected to have a high ionic conductivity of over 10⁻⁴ S cm⁻¹. The established model predicted the change in conductivity as a function of chemical composition (x = content of Mo) (Fig. 1b), and the conductivity was found to increase from x = 0 to a higher value, peak at approximately x = 0.3, and then gradually decrease beyond x = 0.4. Because the experimental values followed this trend, the qualitative predictive ability of the model was verified. However, significant differences (by two or more orders of magnitude) in absolute value between the predicted and experimental conductivities were noted, and the model tended to overestimate the predicted conductivity. For example, a conductivity of ∼10⁻⁶ S cm⁻¹ was estimated even for zero-lithium compositions (e.g., around the tie-line between SiO₂ and MoO₃ in Fig. 1a). Therefore, new models with enhanced prediction accuracy must be further developed.

Figure 1.

(a) Color map of the ionic-conductivity predictions for the Li₂O–SiO₂–MO₃ ternary diagram. (b) Comparison of the predicted and experimental ionic conductivities of Li_4−2xMo_xSi_1−xO₄, which corresponds to the tie-line composition between Li₄SiO₄ and Li₂MoO₄, based on the random forest regression model. The dashed line and circles represent the prediction and experimental results, respectively.

The present study is based on the previously constructed prediction model and aims to develop a model demonstrating improved prediction accuracy by scaling up the learning dataset (∼2200 oxide entries) and adopting various learning algorithms. Features for regression analysis, especially configuration entropy,¹⁴ which could be strongly related to the ionic conductivity of a material with a complex composition,^15–17 were also redesigned and added. Following the building of models that showed high prediction accuracy for the training data, the conductivities of the Li₂O–SiO₂–MO₃ ternary diagram were predicted once more to demonstrate the power of the machine learning models developed in this study.

2. Experimental

Random forest, the algorithm employed in a previous study, was selected to demonstrate the regression analysis between chemical compositions and ionic conductivities¹³ because it is frequently used in the machine learning of inorganic materials^18–20 and offers favorable characteristics, such as the interpretability of feature contributions in the established model. However, given our aim of improving the prediction accuracy of the machine learning model further, we sought to select a more accurate algorithm by running several of the many algorithms that can be implemented in scikit-learn²¹ (e.g., linear regression, decision tree, natural gradient boosting, Gaussian process) as well as relatively new algorithms.^22,23 Multiple algorithms were used to predict conductivity using the incremented learning data and redesigned features described below. Subsequently, we performed conventional model training and testing, as in the machine learning process, and selected those models with exceptionally high prediction accuracy.

For the explanatory variables, numerical values were comprehensively generated for each chemical composition through chemical formulas and statistical processing (e.g., mean, variance, standard deviation, mean of squares) and used as features.¹³ The values of electronegativity,^24,25 valence,²⁶ crystal radii,²⁶ effective ionic radii,²⁶ number of electrons in orbitals,²⁷ melting and boiling points,²⁸ density,²⁸ orbital radii,^29–31 covalent bond radii,³² polarizability,³³ Mendeleev number,^34,35 and chemical scale^34,35 were referenced from the literature. In this process, the physical meaning of each feature was not carefully considered, and no explanatory features specific to ion conductors were introduced. For statistical processing, the new models excluded standard deviation as a feature because this statistic is calculated as the square root of the variance, resulting in a high correlation with variance. On the other hand, geometric mean was added as a new operation for feature generation. This addition was motivated by the use of the geometric mean for calculating electronegativity in terms of atomic nodal radii (“nodalen”) as discussed later. The geometric mean of values reflecting physical properties was also considered a potentially physically meaningful variable.

In addition to the previously adopted features, new features were introduced in this study. First, configurational entropy (“entropy”) was added because the positive effects of compositional complexity, inspired by high-entropy alloys, have been reported to design highly conductive materials.^15–17 The configuration entropy of each composition was calculated using the reported equation.¹⁴ The search for ionic conductors began with simple salts (e.g., LiBr, LiI, Li₂S) and evolved into complex compounds with increasing conductivity (e.g., Li₃PO₄,³⁶ Li₄SiO₄,³⁷ Li₇PS₆Cl,³⁸ Li₁₀GeP₂S₁₂,¹² Li_9.54Si_1.74P_1.44S_11.7Cl_0.3³). Considering this history, compositional complexity may be an excellent explanatory feature. Another feature, nodalen, which was found to correlate empirically with ionic conductivity when considering ionic conductors in glass, was also adopted.³⁹ The values for this feature were calculated from the geometric mean of the chemical composition for each learning data. Another feature was designed to explicitly represent the elemental information of the material; this variable was based on the elemental composition calculated from the chemical formula and is normalized so that the sum of all values equals 1.

In general, a single chemical composition generates 915 features using the data summarized in Table 1. The procedure for deriving features is as follows. For the 42 types of elemental information (e.g., effective ionic radius and polarizability), four static values, including average, mean square, variance, and geometric mean, were calculated. Entropy and nodalen were determined for any given composition based on their respective formula.^14,39 These values were also calculated for five chemical composition patterns: the complete composition, the composition excluding lithium, the composition of cations only, the composition of cations excluding lithium, and the composition of anions only. Here, 850 features were generated. By adding the concentration ratios of 65 elements, a total of 915 features were assigned to a single composition.

Table 1. Symbols and names of the elements used to generate features for the models.

Symbols	Feature name	Symbol	Feature name
atnum	Atomic number	dens	Density of simple substance
atwt	Atomic weight	rs	s orbital radii
en	Electronegativity	rp	p orbital radii
val	Valence	rd	d orbital radii
cr	Crystal radii	rsp	= rs + rp
ir	Effective ionic radii	rspd	= rs + rp + rd
cV	= pi × cr3	Vs	= pi × rs3
iV	= pi × ir3	Vp	= pi × rp3
potentcr	= val/cr	Vd	= pi × rd3
potentir	= val/ir	Vsp	= pi × rsp3
metal	Metal or not	Vspd	= pi × rspd3
hal	Halogen or not	potentrs	= val/rs
typmetal	Typical metal or not	potentrsp	= val/rsp
trnsmetal	Transition metal or not	potentrspd	= val/rspd
li	Lithium or not	r	Covalent (metal) bond radii
s	Number of electrons in s orbital		in simple substance
p	Number of electrons in p orbital	V	= pi × r3
d	Number of electrons in d orbital	potentr	= val/r
f	Number of electrons in f orbital	polar	Polarizability
mp	Melting point of simple substance	memnum	Mendeleev number
bp	Boiling point of simple substance	cs	Chemical scale

The objective variable was the logarithmic ionic conductivity at approximately 300 K. Because the ionic conductivity data used for machine learning spans about 20 orders of magnitude, the correlation between logarithmic conductivity and chemical composition was learned. Data for ∼2200 previously reported chemical compositions and the ionic conductivities of various lithium conductors were used as training data. When several training datasets with the same chemical composition exist, the logarithmic median value of ionic conductivity was calculated and used as the training data for a unique chemical composition.

The reported prediction model revealed two issues: (1) low prediction accuracy for ionic conductivity and a tendency to produce overestimated predictions and (2) prediction of ionic conductivity even for lithium-free compositions. These issues may be explained as follows. All the study data were extracted from studies on lithium conductors, and the chemical compositions described in these papers were usually concentrated in regions of relatively high ionic conductivity. Thus, the model may not predict low ionic conductivities because it did not learn the data of insulating materials. In particular, machine learning models do not understand a fact that is evident to humans: lithium-free compositions do not exhibit lithium-conductive properties. To solve this problem, we added several simple lithium-free oxides to the training data as compositions with ionic conductivities of 10⁻³⁰ S cm⁻¹ (i.e., dummy data for insulators). A summary of the number of constituent elements and the logarithmic ionic conductivity of the materials used in machine learning is shown in Fig. S1. While there are differences due to the number of constituent elements, the majority of the data exhibit conductivities of at least 10⁻²⁰ S cm⁻¹, and both the mean and median values are above 10⁻¹⁵ S cm⁻¹. Therefore, based on the criterion of being less than half of this value, the ionic conductivity of insulating materials was tentatively set to 10⁻³⁰ S cm⁻¹. The dataset was split into training and test data using the Kennard–Stone algorithm.⁴⁰ The filter and wrapper (Boruta⁴¹) methods⁴² were applied to all 915 features generated in this study to reduce them using only the training data. As a result, 88 features were ultimately selected for use in the machine learning process. The hyper-parameters were optimized by black-box optimization⁴³ via random 5-fold cross-validation to build the models.

3. Results and Discussion

3.1 Construction and evaluation of the machine learning models

Ten representative algorithms were examined in this study; NGBoost²² and LightGBM²³ used the libraries reported in the respective papers, and all other models were implemented in scikit-learn.²¹ In Fig. 2, the prediction data of each algorithm (log(σ_pred./S cm⁻¹)) are plotted as a function of the labeled data (log(σ_true/S cm⁻¹)). The results for both the training and test data are also displayed in the figure. The models generally exhibited high prediction accuracy when the data aligned along the diagonal line shown in the figure. Linear regression (a), support vector regression (f), ridge regression (g), and partial least-squares regression (h) are unsuitable for the current objective of high prediction accuracy, as many points deviate significantly from the diagonal. Decision tree (e) and Gaussian process regression (i) fit the training data well but show overfitting as they do not adequately generalize the test data. By contrast, the decision tree-based algorithms (i.e., NGBoost (b), random forest (c), LightGBM (d)) and multilayer perceptron (j) demonstrate high compatibility with both the training and test data. Hence, among the algorithms considered, we selected the decision tree-based algorithms for model building owing to their high interpretability, and proceeded to examine LightGBM and NGBoost, which offer high prediction accuracy and are superior alternatives to random forest.¹³

Figure 2.

Predictive capabilities of 10 regression algorithms illustrated as scatter plots correlating true and predicted conductivity values at the logarithmic scale: (a) Linear regression, (b) NGBoost, (c) random forest, (d) LightGBM, (e) decision tree, (f) support vector regression, (g) ridge regression, (h) partial least-squares regression, (i) Gaussian process regression, and (j) multilayer perceptron. The black triangles and red circles indicate the results obtained from the training and test data, respectively.

The Random Forest method used in the previous study, as well as NGBoost and LightGBM employed in this study, are all decision tree-based algorithms. A key characteristic of NGBoost and LightGBM is that they construct decision trees using gradient descent to minimize errors. This approach enables higher prediction accuracy compared to Random Forest, which generates decision trees randomly for training. Furthermore, a comparison between NGBoost and LightGBM reveals that NGBoost has the advantage of accounting for the uncertainty of prediction results. In regression learning, NGBoost not only minimizes the error of regression values but also optimizes the model by considering uncertainty. Consequently, the output includes not only the predicted regression values but also an uncertainty index. However, despite being a powerful algorithm, NGBoost has the drawback of requiring longer computational time for machine learning processes. On the other hand, while LightGBM does not provide uncertainty estimates, it offers the advantage of performing high-accuracy predictions at a significantly faster speed. Therefore, selecting the appropriate algorithm based on the specific application is crucial.

The accuracies of the developed models were quantitatively evaluated using error functions (RMSE and MAE) and coefficients of determination (R²), as summarized in Table 2. As confirmed in Fig. 2, LightGBM and NGBoost show high prediction accuracy. The MAE values for the test data suggest that the constructed models can, on average, predict log ionic conductivity within an error range of less than 0.5. Given this value, the absolute mean error in ionic conductivity may be expected to fall within the range between a factor of 0.31 and 3.16, which means the average prediction error would fall within plus or minus one order of magnitude, indicating the relatively high prediction accuracy of the models.

Table 2. Prediction performance indices of the NGBoost and LightGBM models.

	MAE		RMSE		R2
	Training	Test	Training	Test	Training	Test
NGBoost	0.32	0.45	0.90	0.70	0.96	0.74
LightGBM	0.35	0.49	0.65	0.73	0.98	0.65

The RMSE values were slightly higher than the MAE values in both models. Because RMSE is more sensitive to outliers than MAE, outliers may be present in the predictions of the models. However, the RMSE values for the test data were below 0.8, which is a significant improvement compared with the previously reported value of 1.65.¹³ Therefore, the predictive accuracy of the new models can be considered significantly improved.

A comparison of the RMSE, MAE, and R² values for the training and test data revealed poorer values for most of the testing data than for the training data. This finding implies that the constructed models could have overlearned the training data. The change in the values of the loss function relative to the number of learning sessions was confirmed to verify the status of over-fitting (Fig. 3). The behavior of the loss function of the training data depending on the number of training sessions showed a sharp decrease in the initial process in both models, and the rate of decrease eased as training progressed. The continuous downward trend of the loss function suggests that learning proceeds smoothly on the training data. Compared with those for the training data, the changes in the loss function for the test data behaved slightly differently in both models. However, after the learning process, no upward trend in the loss function for the test data was observed. In the case of over-fitting, the loss function for the training data would continue to decrease, while the loss function for the test data begins to increase. Therefore, serious over-fitting does not appear to occur in these models. To improve the test data score relative to the training data score, since both NGBoost and LightGBM are algorithms based on decision trees, possible approaches include reducing the depth of the trees or decreasing the number of nodes. However, excessive concern about preventing over-fitting may instead lead to a deterioration of the training data score and result in under-fitting. Therefore, we did not conduct such verification in this study.

Figure 3.

Relationship between the number of iterations and loss function value for the (a) NGBoost and (b) LightGBM models.

Table 3 lists the top 15 features with the greatest importance for each model. The most important feature in both models was lithium content, the importance of which was over 10 times that of the features ranked second and lower. This result could be due to the training of the model with lithium-free metal oxides as insulators. In the models, lithium-free metal oxides were considered to have much lower conductivity (10⁻³⁰ S cm⁻¹) than conventional lithium conductors (>10⁻¹⁰ S cm⁻¹). Because the training data were intentionally modified, the model is unlikely to accurately recognize the importance of subtle changes in lithium content caused by the formation of solid solutions or elemental substitutions. The fact that the importance of Li content is much higher than that of other features supports this hypothesis. Therefore, the handling of lithium-free materials requires further investigation.

Table 3. Top 15 features with the greatest importance for the NGBoost and LightGBM models.

NGBoost		LightGBM
Feature	Importance (%)	Feature	Importance (%)
Content ratio of Li	33.5	Content ratio of Li	50.8
Mean of “d” (c)	3.1	“entropy” (c, l)	4.6
Variance of “Vspd” (c, l)	3.0	Variance of “Vspd” (c, l)	4.0
Mean squared of “d” (c)	2.9	Mean of “d” (c)	3.5
“entropy” (c, l)	2.5	Content ratio of O	1.7
Variance of “family” (c, l)	1.6	Mean squared of “d” (c)	1.5
Mean squared of “s” (c)	1.3	Variance of “val” (c, l)	1.2
Geometric mean of “Vspd” (c)	1.1	Variance of “mp” (c, l)	1.0
Geometric mean of “val” (c, l)	1.1	“entropy” (l)	0.9
Variance of “bp” (c)	1.1	Mean squared of “s” (c)	0.9
Content ratio of Si	1.0	Mean squared of “cs” (l)	0.9
Mean squared of “typmetal” (l)	1.0	Variance of “s” (c)	0.9
Content ratio of Co	1.0	Mean squared of “iV”	0.8
“entropy” (l)	1.0	Variance of “metal” (c)	0.8
Content ratio of Zr	1.0	Variance of “Vs” (c, l)	0.8

The features are based on the symbols in Table 1. The legends “c” and “l” after a feature name indicate that the value was calculated for the composition of only cations and excluding lithium, respectively.

An interesting finding for both models is that “entropy of cations excluding lithium” has high importance, ranking 5th (2.5 %) for NGBoost and 2nd (4.6 %) for LightGBM. “Entropy excluding lithium” was also highlighted, ranking 14th (1.0 %) for NGBoost and 9th (0.9 %) for LightGBM. These trends support the historical development of materials by introducing different elements into the framework of ionic conductors to enhance their ionic conductivity. In other words, the results suggest the usefulness of material design through high-entropy strategies, which have recently garnered increased attention.^15–17 An analysis of the relationship between the number of constituent elements in the materials used for machine learning and the logarithm of ionic conductivity (Fig. S1) reveals that, while the data number and variance vary depending on the number of elements, the mean value exhibits a continuous increase from binary to heptary systems. Likewise, the median value also demonstrates a consistent upward trend from binary to senary systems. The machine learning model developed in this study successfully captures a strong correlation between compositional complexity and ionic conductivity based on the training data. This suggests that the model effectively recognizes the impact of compositional complexity on ionic transport properties. On the other hand, nodalen, which was similarly introduced into the models, was not recognized as an important explanatory variable, possibly because this factor explains empirical rules for amorphous materials,³⁹ which are of low concern when applied to data mainly concerning crystalline materials. In addition, if the lithium-free metal oxides data with extremely low ionic conductivity (10⁻³⁰ S cm⁻¹) were excluded in training, the importance of lithium content significantly decreased in the feature ranking (Table S1). However, there were no major changes in the top-ranked features, and their relative importance increased. Therefore, the impact of lithium-free metal oxides data on the machine-learning model is limited.

The NGBoost model recognized the content of specific elements (e.g., contents of Si and Zr) as important features, while the LightGBM model tended to recognize physical quantities such as melting point, valence, and ionic radius, which are not specific to particular element types, as important features. The variation in the feature importance rankings between these models could depend on the differences in the learning methods of the two algorithms. Qualitatively, NGBoost is expected to capture changes in ionic conductivity more accurately when specific elements are introduced into the target material. Meanwhile, LightGBM is expected to be useful for selecting compositions with high ionic conductivity from a broad compositional space. Thus, these two models could be utilized selectively depending on the objectives and phase of progress in materials discovery research.

Here, we discuss the differences between the two models. NGBoost learns not only regression values but also considers probability distributions. In other words, it optimizes the model by considering not only regression errors but also uncertainty. Consequently, unlike LightGBM, which prioritizes the rapid minimization of regression errors, NGBoost may result in differences in the ranking of explanatory variable importance. Regarding model selection, considering the differences in algorithms, NGBoost is more suitable when it is necessary to account for prediction uncertainty. Conversely, if the primary objective is to achieve faster predictions, LightGBM should be chosen. Furthermore, when focusing on differences in features, NGBoost is preferable for systems incorporating specific elements (i.e., elemental doping approach). In contrast, LightGBM is more suitable for broader explorations within pseudo-ternary phase diagrams.

3.2 Feasibility of the developed machine learning models

The predictive abilities of the new models were assessed by comparing their prediction results for the Li_4−2xSi_1−xMo_xO₄ system with those of a previous paper and experimental results,¹³ as shown in Fig. 4a. The NGBoost model demonstrated a trend of improved ionic conductivity with increasing Mo content (x) for compositions below 0.3. In this compositional range, the difference between the experimental and predicted values was within two orders of magnitude, indicating high consistency. However, the predicted conductivity dropped sharply as x approached 0.4. The difference in log σ at x = 0.4 increased to approximately −3.5, but still showed a higher level of agreement than previously reported models (Δ log σ = ∼5.0). NGBoost is a nonlinear model based on decision trees. Therefore, it can make predictions that do not have a linear relationship with chemical composition or lithium content. The predictions of NGBoost show a significant change around x = 0.4, suggesting the presence of a threshold at this composition. As a result, the conductivity remained nearly constant for compositions with x ≥ 0.4.

Figure 4.

Ionic-conductivity predictions for the Li₂O–SiO₂–MO₃ ternary diagram. Compositional dependence in (a) Li_4−2xMo_xSi_1−xO₄ and (b) (1 − x)Li₂Si₉O₁₉–xLi₂Mo₉O₂₈. The experimental values and prediction data from Ref. 10 are also indicated.

Predictions derived from the LightGBM model demonstrated even higher accuracy, with the difference from the experimental values, Δ log σ, remaining within a range of less than 1.5. Thus, the new models were confirmed to provide predicted values close to the experimental values in all cases, corresponding to significant improvements in error function values (RMSE, MAE) against the test data. Although the new models were trained with a large amount of data, the experimental data for the Li–Si–Mo–O system were not included in the machine learning dataset. The difference in prediction accuracy between the models could be due to differences in the learning methods of the two algorithms. In cases such as that examined in this paper (Li_4−2xSi_1−xMo_xO₄), where predictions over a wide compositional range are required, the LightGBM model, which is less sensitive to the content of specific elements, may be more suitable.

Figure 4b compares the predicted ionic conductivity for chemical compositions with low lithium content: (1 − x)Li₂Si₉O₁₉–xLi₂Mo₉O₂₈. Based on experience and intuition, compositions with very low lithium contents can be predicted to exhibit extremely low ionic conductivity. According to the Nernst-Einstein equation,⁴⁴ ion conductivity depends on both the carrier ion concentration and its diffusion coefficient. Therefore, in chemical compositions with a low lithium content, the carrier ion number density decreases, leading to a tendency for lower conductivity. In an extreme case, if the composition does not contain lithium ions, the lithium ion conductivity becomes zero. However, the previous model predicted the ionic conductivity of the dominant composition region to be approximately 10⁻⁶ S cm⁻¹. Remarkably, the highest value exceeded 10⁻⁴ S cm⁻¹ at approximately x = 0.7.¹³ By contrast, the new models successfully estimated low ionic conductivity for these compositions. The NGBoost and LightGBM models predicted values lower than 10⁻⁸ S cm⁻¹ and 10⁻⁷ S cm⁻¹, respectively. As no experimental values exist for the predicted hypothetical chemical compositions, which model provides the most accurate predictions quantitatively cannot be evaluated at present. However, compared with the previous model, which predicted ionic conductivities comparable with those of typical ionic conductors even in compositions with minimal lithium content, the predictions of the new models align more closely with a chemist’s intuition. This result could be attributed to various factors, including the use of a larger number of datasets, redesigned features, adoption of new algorithms, and the training of the models to treat lithium-free compositions as insulators (10⁻³⁰ S cm⁻¹). These adjustments clearly improved the prediction accuracy of the models, particularly by suppressing the overestimation of ionic conductivity. In practice, when using models that were not trained on lithium-free metal oxides data to predict compositions with low lithium content ((1 − x)Li₂Si₉O₁₉–xLi₂Mo₉O₂₈.), it tended to predict relatively high ionic conductivities, leading to overestimation (Fig. S2). In particular, significant deviations in ion conductivity predictions were observed in the LightGBM models. From these findings, although this may not be the optimal approach, it was found that including dummy data of lithium-free metal oxides in the training process is necessary to suppress the overestimation of ionic conductivity.

In the binary LISICON system (Li_4−2xSi_1−xMo_xO₄), where prediction accuracy issues had been pointed out in the previous report,¹³ this study demonstrated that the constructed model provides more accurate predictions. From this point, we proceeded to evaluate the generalization performance of the developed models. The conductivities of quasi-ternary lithium superionic conductor (LISICON) materials were predicted to assess the feasibility of the constructed models for more complex chemical compositions, which may contain unknown highly conductive materials. A comparison of the reported values⁴⁵ with the model predictions is depicted in Fig. 5. The background color of the triangular phase diagram represents the predicted ionic conductivity. Notably, the conductivity data of quasi-ternary Li₃VO₄–Li₄GeO₄–Li₄SiO₄ were not included as learning data for this prediction trial. Given this type of phase diagram, extensive research has been conducted on LISICON materials corresponding to the binary systems along the edges of the triangle.⁴⁶ By contrast, the interior regions of the triangle remain unexplored and represent compositionally complex systems that have recently gained attention.^15,46–48

Figure 5.

Ionic-conductivity predictions by the (a) NGBoost and (b) LightGBM models and experimental results for quasi-ternary Li₃VO₄–Li₄GeO₄–Li₄SiO₄.

Both models predicted high ionic conductivity within the interior regions of the triangle. Each side of the triangle corresponds to a binary solid solution of the LISICON. In particular, the region around the Li₄GeO₄–Li₃VO₄ binary system was predicted to exhibit the highest ionic conductivity owing to the Li₄GeO₄–Li₃VO₄ solid solution having the highest conductivity (∼10⁻⁵ S cm⁻¹)⁴⁶ among the binary systems. Furthermore, the results suggest that adding Si to this solid solution could increase its conductivity. A comparison of these predictions and the experimental values indicated by the circles in the diagram reveals excellent agreement. Notably, the predicted values are very close to those of the LightGBM model.

Although the predictions do not align perfectly with experimentally observed ionic conductivities, they suggest the potential for improved conductivity in more compositionally complex pseudo-ternary regions. This prediction trend is likely due to the introduction of configurational entropy as a new feature, which the machine learning models recognized as an important feature. Therefore, utilizing the machine learning models developed in this study may enable the more efficient exploration of new materials with complex chemical compositions. Furthermore, because the region near Li₄SiO₄ is not predicted to exhibit high ionic conductivity, it can be excluded from the exploration targets, enabling more efficient searches for ternary materials. The developed machine learning models are currently limited to predicting oxide-based materials. However, by accumulating training data for sulfides, halides, and other materials, as well as improving the algorithms and features, a more generalizable model is expected to be developed. The next-generation models based on this study could be valuable for selecting constituent elements and chemical compositions when introducing additional elements into known electrolyte materials, such as Li₁₀GeP₂S₁₂^16,49- and argyrodite^50,51-type compounds.

4. Conclusions

We developed machine learning models to predict ionic conductivity with high accuracy based solely on chemical composition information. Using a dataset of ∼2200 entries for learning, we performed regression learning with multiple algorithms. Two decision tree-based algorithms, NGBoost and LightGBM, demonstrated exceptionally high prediction accuracy. According to the MAE values for the test data, the constructed models can, on average, predict the absolute mean error in ionic conductivity within the range between a factor of 0.31 and 3.16. The developed models recognized entropy as an important feature, aligning with the historical development of ionic conductors and the recent trend toward compositional complexity. The developed models demonstrated excellent prediction performance even for pseudo-binary systems such as Li_4−2xSi_1−xMo_xO₄ and pseudo-ternary systems such as Li₄SiO₄–Li₄GeO₄–Li₃VO₄, which had not been included in the training data for machine learning. The established models are expected to facilitate efficient material discovery for developing all-solid-state lithium batteries. Future research could focus on further increasing the training data and incorporating sulfide and halide materials into the learning process to enhance the generalizability of these models.

Acknowledgments

The authors were waived from the APC with the support of The Committee of Battery Technology, ECSJ.

Data Availability Statement

The data that support the findings of this study are openly available under the terms of the designated Creative Commons License in J-STAGE Data at https://doi.org/10.50892/data.electrochemistry.28427960.

• 1) A machine learning model that can predict the ionic conductivity of lithium-containing oxides using chemical composition and ionic conductivity data was previously developed. However, this model revealed several limitations, leading to less-than-ideal prediction accuracy. Thus, new models demonstrating improved prediction ability must be developed. This study presents the development of machine learning models for the accurate prediction of ionic conductivity in lithium-containing materials based solely on their chemical composition. The models constructed using the NGBoost and LightGBM algorithms show high compatibility with the training and test data, resulting in high predictive accuracy. The constructed models identify “entropy,” which is considered a key factor in developing ionic conductors, as an important feature. This finding highlights the potential utility of this property from a solid-state chemistry perspective. The developed models demonstrate high predictive accuracy even for previously reported lithium superionic conductor-type materials that were not included in the training dataset. The established models are expected to facilitate efficient material discovery for the development of all-solid-state lithium batteries.

CRediT Authorship Contribution Statement

Yudai Iwamizu: Data curation (Lead), Formal analysis (Lead), Investigation (Lead), Methodology (Lead), Writing – original draft (Lead)

Kota Suzuki: Conceptualization (Lead), Funding acquisition (Equal), Project administration (Equal), Supervision (Equal), Writing – review & editing (Lead)

Michiyo Kamiya: Data curation (Supporting), Writing – review & editing (Supporting)

Naoki Matsui: Data curation (Supporting), Writing – review & editing (Supporting)

Kuniharu Nomoto: Data curation (Supporting), Writing – review & editing (Supporting)

Satoshi Hori: Data curation (Supporting), Writing – review & editing (Supporting)

Masaaki Hirayama: Conceptualization (Equal), Supervision (Equal)

Ryoji Kanno: Conceptualization (Equal), Supervision (Equal)

Conflict of Interest

There is no conflict of interest.

Funding

Advanced Low Carbon Technology Research and Development Program: JPMJAL1301

Precursory Research for Embryonic Science and Technology (JP): JPMJPR17N7

Program on Open Innovation Platform with Enterprises, Research Institute and Academia: JPMJOP1862

Japan Society for the Promotion of Science: 19H05785

Japan Society for the Promotion of Science: 24H00042

Footnotes

A part of this paper has been presented in the 65th Battery Symposium in Japan in 2024 (Presentation #2F15).

K. Suzuki, N. Matsui, K. Nomoto, S. Hori, M. Hirayama, and R. Kanno: ECSJ Active Members

R. Kanno: ECSJ Fellow

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