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Shang et al. J. Mater. Inf. 2025, 5, 52 https://dx.doi.org/10.20517/jmi.2025.36 Page 5 of 15

Construction of SISSO descriptors
After completing feature engineering, we implemented SISSO to systematically identify optimal descriptors
demonstrating strong correlations with work function. SISSO is a “glass-box” ML model that is designed to
address the challenges of high-dimensional data and feature selection . In this context, it identifies both
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linear and nonlinear relationships between input features and target properties, offering insights into the
mechanisms influencing the work function of MXenes.

During the discovery of descriptors, the mathematical operators H = {“−, *, /, ^-1, ^2, ^3, sqrt, exp,” etc.}
were used in constructing the descriptors. Herein, the parameter “fcomplexity”, representing the number of
operators, was typically set between 0 and 7. With these settings, the descriptor sets including 35,822,
630,070, 78,025,280, 2,033,702,714, 36,517,309,938, and 287,772,622,033 descriptors were generated in
fcomplexity of 2, 3, 4, 5, 6, and 7, respectively. They represent the number of descriptors generated by SISSO
models in different complexity, whose accuracy increases with increasing complexity. To evaluate the
performance across different model complexities (fcomplexity), we conducted a systematic analysis of the
SISSO-generated features by comparing the average correlation of the top 20 features (with respect to the
work function) against the computational time. Specifically, as fcomplexity increased from 1 to 7, the
average correlation progressively improved (0.300 at fcomplexity = 1, 0.816 at fcomplexity = 5, and 0.848 at
fcomplexity = 7, respectively), indicating that higher complexities produce more relevant descriptors.
However, the computational consumption increased almost exponentially, from 0.8 seconds at fcomplexity
= 1, escalating to 966 seconds at fcomplexity = 5, and surging to about 17.2 kiloseconds at fcomplexity = 6
and 37.9 kiloseconds at fcomplexity = 7 (details in Supplementary Figure 1), respectively. Given that the
correlation gains plateau after fcomplexity = 5 while the computational overhead intensifies sharply, we
selected fcomplexity = 5 as the optimal descriptor, thereby achieving an effective balance between feature
relevance and computational efficiency . Therefore, it is reasonable that the descriptor at fcomplexity = 5 is
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selected as the optimal descriptor . At a fcomplexity of 5 (see Supplementary Table 2 for additional
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parameters), 1,000 candidate descriptors were successfully generated. These descriptors are derived from the
original features based on predefined mathematical operators, thereby ensuring complete transparency.

ML model design
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In this section, we constructed a stacked model using the RF model as the meta-model, while the gradient
boosting tree (GB) , support vector regression (SVR) , extreme gradient boosting tree (ET) , and K
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nearest neighbor regression (KNR) were selected as the base models. Stacked models, built using a
stacking architecture, endow meta-models with the ability to integrate the predictive outputs of the base
models, incorporating multiple patterns and insights that may be difficult for a single algorithm to achieve
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on its own . As shown in Figure 2A, the general RF model exhibits an MAE of 0.25 with a R of 0.91 after
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optimizing the parameters through grid search and 5-fold cross-validation [44,45] . Comparably, the stacked
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model possesses a lower MAE (0.22) and higher R (0.94) under the same parameter tuning conditions
[Figure 2B], demonstrating that the layering strategy can achieve significantly improved performance.
Furthermore, we have further combined the prediction data of the general RF model and the stacked model
in Figure 2C. Upon comparison, it is evident that the prediction points of the general RF model within the
purple box deviate significantly from the prediction line, indicating these points are potential outliers or in
areas of reduced prediction accuracy. While after the integration of base models, the prediction points
noticeably move closer to the prediction line. In order to further demonstrate the superior capability of
stacked model in handling outliers, we have evaluated an alternative meta-model, GBDT, through five-fold
cross-validation. The results are shown in Supplementary Figure 2, indicating that in Supplementary Figure
2A, B, D, and E, the predictions (blue circles) of stacked model for the same data points are markedly closer
to the perfect prediction line than those of the general GBDT model (red triangles), which can be evidenced
by reduced scatter and lower MAE values (e.g., 0.2026 vs. 0.2468 in fold 1). Even in Supplementary Figure