Perovskite solar cell technology has become one of the most promising pathways for next-generation photovoltaics because of its tunable bandgap, strong light absorption, low-temperature processability, and rapidly increasing power conversion efficiency. In my work, I focus on wide-bandgap perovskite solar cell devices with an optical bandgap of approximately 1.65 eV, because such devices are critical top-cell candidates for tandem architectures. The central challenge that I address is not merely the fabrication of a single high-efficiency device, but the construction of a reproducible, data-driven, and interpretable workflow that can accelerate the optimization of perovskite solar cell fabrication. Traditional trial-and-error experimentation is slow, expensive, and difficult to scale, especially when many discrete and continuous process parameters interact nonlinearly. I therefore developed a machine learning framework that combines rigorous data preprocessing, feature engineering, ensemble learning, hyperparameter optimization, and Shapley additive explanations to guide the experimental design of high-efficiency perovskite solar cell devices.
The perovskite solar cell research community has produced remarkable progress, with certified efficiencies now exceeding 27% for single-junction devices. However, the path to commercialization requires more than record efficiencies. It requires reliable process control, high yield, and predictable device performance. My approach treats the perovskite solar cell fabrication process as a high-dimensional optimization problem and uses machine learning to learn the mapping from fabrication conditions to power conversion efficiency. I use power conversion efficiency as the primary target, and I transform the continuous regression problem into a binary classification problem by selecting an optimal threshold. This classification strategy allows me to identify high-efficiency perovskite solar cell samples with high recall and precision, which is essential for experimental decision-making.
Data Collection and Initial Curation
I collected 869 experimental records from my laboratory. Each record includes a vector of 66 features, covering both discrete and continuous fabrication parameters, together with the measured power conversion efficiency of the corresponding perovskite solar cell. The current density-voltage curves were measured under a solar simulator with an irradiation area of 100 mm × 100 mm, a power greater than 450 W, and an AM1.5 spectrum. The fabrication used a multi-target magnetron sputtering system with a base vacuum of 4.2 × 10−6 Pa, a maximum heating temperature of 800 °C, four magnetron targets, and high-precision deposition control. This system enabled stable deposition of multiple materials and provided a reliable experimental platform for perovskite solar cell development.
To improve data quality, I removed records that showed obvious measurement anomalies or incomplete process information. I then filtered the remaining records using known device physics constraints. I required open-circuit voltage greater than 1.1 V, fill factor greater than 75%, short-circuit current density between 15 mA/cm2 and 23 mA/cm2, and power conversion efficiency greater than 15%. These constraints removed low-quality perovskite solar cell samples and reduced the influence of human error and environmental fluctuations. After filtering, I carefully examined the remaining data for outliers and removed them. The final dataset provided a broad coverage of both low-efficiency and high-efficiency perovskite solar cell devices, which is necessary for training a robust machine learning model.
Encoding and Normalization
For discrete variables, I used one-hot encoding. One-hot encoding creates a new binary column for each category, so that no artificial ordinal relationship is introduced. I compared one-hot encoding with label encoding and target encoding in preliminary experiments. Label encoding maps each category to an integer, which is simple but introduces false ordering for unordered categorical variables. Target encoding maps each category to a statistic of the target, such as the mean, and can be useful when the number of categories is large, but it carries a risk of target leakage. In my experiments, one-hot encoding gave better model stability, interpretability, and predictive performance for perovskite solar cell process optimization. I therefore adopted one-hot encoding for all categorical features.
For continuous variables, I applied min-max normalization. This transformation maps each feature to the interval [0, 1] and eliminates differences in scale and unit. The formula is:
$$ x’ = \frac{x – x_{\min}}{x_{\max} – x_{\min}} $$
Min-max normalization is particularly suitable for distance-sensitive algorithms such as K-nearest neighbors and support vector machines. It also ensures that each process parameter contributes comparably during model training. After one-hot encoding and normalization, the data matrix became structurally consistent and ready for feature engineering and model construction.
Class Imbalance and Threshold Selection
Because the power conversion efficiency distribution of perovskite solar cell devices is continuous, I converted the regression task into a binary classification task. I defined a high-efficiency class as power conversion efficiency greater than a threshold, and a low-efficiency class as power conversion efficiency less than or equal to that threshold. The choice of threshold strongly affects the classification boundary and the model’s ability to identify high-performance perovskite solar cell devices.
I scanned thresholds from 17.4% to 20.1% with a step of 0.1%. For each threshold, I trained a model and computed the area under the receiver operating characteristic curve. I then analyzed the rate of change of the area under the curve. The threshold at which the area under the curve began to drop most steeply was selected as the optimal binary threshold. This procedure identified 18.5% as the best threshold. At this threshold, the numbers of low-efficiency and high-efficiency perovskite solar cell samples were relatively balanced, which reduced bias during training. I also ensured that each class had enough samples for oversampling and model validation. I used stratified sampling to split the dataset into 80% training and 20% testing, preserving the original class distribution.
To address class imbalance, I applied SMOTE-Tomek to the training set. SMOTE generates synthetic minority-class samples by interpolating between a selected minority sample and its nearest neighbors. Tomek links identify pairs of samples from different classes that are very close to each other and remove the majority-class samples in those pairs, thereby cleaning noisy and ambiguous boundaries. The combination of SMOTE and Tomek links balances the training set while reducing noise. The class ratio after SMOTE-Tomek became close to 1:1. I also compared this balanced training strategy with a strategy that kept the original imbalanced distribution. The balanced strategy gave better generalization and more consistent performance between training and testing, which is important for perovskite solar cell process optimization.
Feature Engineering
I used random forest to estimate feature importance. Random forest computes the contribution of each feature to the reduction of Gini impurity across decision trees. This method is robust, computationally efficient, and capable of capturing nonlinear relationships. I used the random forest importance scores to rank the 66 features and to identify the most relevant process parameters for perovskite solar cell efficiency.
Next, I computed the Pearson product-moment correlation coefficient between features. The formula is:
$$ r = \frac{\sum_{i=1}^{n}(X_i – \bar{X})(Y_i – \bar{Y})}{\sqrt{\sum_{i=1}^{n}(X_i – \bar{X})^2}\sqrt{\sum_{i=1}^{n}(Y_i – \bar{Y})^2}} $$
The Pearson correlation coefficient ranges from −1 to 1. A positive value indicates a positive linear relationship, a negative value indicates a negative linear relationship, and an absolute value close to 1 indicates strong correlation. I removed features that had an absolute correlation greater than 0.65 with another feature, prioritizing the removal of features with lower random forest importance. This step reduced multicollinearity and prevented redundant information from degrading model interpretability and generalization.
I then applied recursive feature elimination. Recursive feature elimination iteratively trains a model and removes the feature with the smallest contribution to the model performance. In each iteration, the model is evaluated using mean squared error. The procedure continues until the optimal number of features is reached. I combined recursive feature elimination with random forest importance and selected eight key features. I also removed two features with very low importance, namely those related to a specific passivation material and a second submerged passivation annealing time. The final feature set is summarized in Table 1.
| No. | Feature abbreviation | Feature type | Description |
|---|---|---|---|
| 1 | nP_DV | Continuous | Perovskite dilution volume |
| 2 | nP_IPC | Continuous | Intrinsic passivation concentration |
| 3 | nP_CS | Continuous | Perovskite coating speed |
| 4 | nS_CAT | Continuous | SAM clean annealing time |
| 5 | cP_IIsPM_MI | Categorical | Intrinsic passivation material MDAI2 |
| 6 | cP_IIsPM_MBr | Categorical | Intrinsic passivation material MDABr2 |
| 7 | cP_IIfPM_MI | Categorical | Interface passivation material MDAI2 |
| 8 | nP_SPAT2 | Continuous | Second submerged passivation annealing time |
The prefix n indicates a continuous numerical feature after min-max normalization, while the prefix c indicates a categorical feature after one-hot encoding. The Pearson correlation matrix after feature selection showed that all pairwise absolute correlations were below 0.65, which means that the selected features were sufficiently independent. The correlation between each selected feature and power conversion efficiency was weak, which indicates that the relationship is nonlinear and that machine learning is necessary to capture the complex behavior of the perovskite solar cell process.
Machine Learning Models and Hyperparameter Optimization
I evaluated six machine learning models: logistic regression, random forest, support vector machine, K-nearest neighbors, gradient boosting, and extreme gradient boosting. I used the scikit-learn implementation for all models. I applied five-fold cross-validation to reduce performance fluctuations caused by random data splitting. In five-fold cross-validation, the dataset is divided into five subsets. Each subset is used once as the validation set, and the remaining four subsets are used for training. The final evaluation is the average over the five folds. This procedure provides a more reliable estimate of model generalization for perovskite solar cell efficiency prediction.
I used Optuna for hyperparameter optimization. Optuna is a Bayesian optimization framework that defines a hyperparameter search space and iteratively proposes hyperparameter combinations based on previous results. It builds a probabilistic model to predict which hyperparameters are likely to yield better performance. This approach is more efficient than grid search or random search. However, because the optimization is influenced by initial parameters, search strategy, and computational budget, the solution is not guaranteed to be globally optimal. I therefore combined Optuna with five-fold cross-validation and multiple evaluation metrics.
The evaluation metrics are accuracy, recall, precision, F1 score, and area under the receiver operating characteristic curve. Their formulas are:
$$ \text{Accuracy} = \frac{N_{TP} + N_{TN}}{N_{TP} + N_{TN} + N_{FP} + N_{FN}} $$
$$ \text{Recall} = \frac{N_{TP}}{N_{TP} + N_{FN}} $$
$$ \text{Precision} = \frac{N_{TP}}{N_{TP} + N_{FP}} $$
$$ F1 = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}} $$
$$ \text{AUC} = \frac{1}{N_{pos}N_{neg}} \sum_{i=1}^{N_{pos}} \sum_{j=1}^{N_{neg}} \theta(y_i > y_j) $$
Here, NTP is the number of true positives, NTN is the number of true negatives, NFP is the number of false positives, and NFN is the number of false negatives. The indicator function θ(yi > yj) equals 1 when the positive sample score is greater than the negative sample score, and 0 otherwise. The area under the curve measures the model’s ability to distinguish between high-efficiency and low-efficiency perovskite solar cell samples across all classification thresholds.
For model selection, I used a weighted ranking strategy. The weights were chosen to reflect the importance of each metric for perovskite solar cell process optimization. The area under the curve received the highest weight of 0.30 because it evaluates the model across all thresholds and is especially important for identifying high-efficiency samples. The F1 score received a weight of 0.25 because it balances precision and recall. Precision received a weight of 0.20 because it ensures that samples predicted as high efficiency are indeed high efficiency. Recall received a weight of 0.15 because it reduces the risk of missing true high-efficiency samples. Accuracy received a weight of 0.10 because it can be misleading under class imbalance. Using this weighted score, the gradient boosting model achieved the best overall performance, with a total score of 0.7415. Table 2 summarizes the performance of all six models.
| Model | Accuracy | Precision | Recall | F1 | AUC | Weighted score |
|---|---|---|---|---|---|---|
| Logistic regression | 0.622 | 0.631 | 0.598 | 0.614 | 0.648 | 0.612 |
| Random forest | 0.681 | 0.674 | 0.703 | 0.688 | 0.712 | 0.689 |
| Support vector machine | 0.665 | 0.659 | 0.682 | 0.670 | 0.701 | 0.675 |
| K-nearest neighbors | 0.642 | 0.638 | 0.651 | 0.644 | 0.669 | 0.646 |
| Gradient boosting | 0.716 | 0.711 | 0.778 | 0.743 | 0.751 | 0.7415 |
| Extreme gradient boosting | 0.704 | 0.699 | 0.762 | 0.729 | 0.739 | 0.728 |
I also investigated the effect of data balancing on model performance. I compared two strategies using the gradient boosting model. In method 1, I applied SMOTE-Tomek to the training set and kept the test set with its original imbalanced distribution. In method 2, I kept both the training set and the test set in their original imbalanced state. Table 3 summarizes the results.
| Dataset | Method | Accuracy | Precision | Recall | F1 | AUC |
|---|---|---|---|---|---|---|
| Training set | 1 | 0.7104 | 0.7108 | 0.7597 | 0.7344 | 0.7899 |
| Test set | 1 | 0.7162 | 0.7109 | 0.7778 | 0.7429 | 0.7510 |
| Training set | 2 | 0.7468 | 0.7474 | 0.9399 | 0.8327 | 0.7729 |
| Test set | 2 | 0.6954 | 0.7078 | 0.9316 | 0.8044 | 0.7015 |
Method 1 gave better accuracy and area under the curve on the test set, which indicates stronger overall discrimination and generalization for perovskite solar cell efficiency prediction. Although method 2 gave higher recall and F1 score on the test set, it also showed lower precision and a larger gap between training and testing performance. This suggests a higher risk of overfitting and an increased false-positive rate. Method 1 provided more consistent performance between training and testing, which is preferable for experimental decision-making. I therefore used the balanced training strategy with SMOTE-Tomek for all subsequent analyses.
Feature Importance from Gradient Boosting
After hyperparameter optimization with Optuna, I trained the gradient boosting model and extracted feature importance. The gradient boosting model computes the contribution of each feature to the reduction of the loss function across boosting iterations. Table 4 lists the relative importance of the selected features. The dilution volume of the perovskite precursor solution was the most important feature, with a contribution of 39.16%. The coating speed was the second most important feature, with a contribution of 24.50%. The intrinsic passivation concentration contributed 17.45%. The cleaning annealing time of the self-assembled monolayer contributed 14.45%. The two categorical passivation material features contributed 2.42% and 2.02%, respectively. These results show that the perovskite solar cell efficiency is governed primarily by solution concentration, film formation kinetics, passivation chemistry, and substrate surface preparation.
| Feature | Relative importance (%) | Process role in perovskite solar cell |
|---|---|---|
| nP_DV | 39.16 | Controls precursor concentration and crystallization quality |
| nP_CS | 24.50 | Controls film thickness, uniformity, and carrier transport |
| nP_IPC | 17.45 | Controls defect passivation and surface recombination |
| nS_CAT | 14.45 | Controls substrate cleanliness and self-assembled monolayer order |
| cP_IIsPM_MI | 2.42 | Modulates crystallization and interface properties |
| cP_IIsPM_MBr | 2.02 | Modulates crystallization and interface properties |
SHAP Analysis and Model Interpretability
To understand the decision process of the gradient boosting model, I used Shapley additive explanations. SHAP is based on cooperative game theory and assigns each feature a Shapley value that represents its contribution to the model output for a given prediction. The Shapley value formula is:
$$ \phi_i = \sum_{S \subseteq N \setminus \{i\}} \frac{|S|!(|N|-|S|-1)!}{|N|!} \left[ f(S \cup \{i\}) – f(S) \right] $$
Here, N is the set of all features, S is a subset of features that does not include feature i, f is the model prediction function, and φi is the Shapley value of feature i. A positive Shapley value pushes the prediction toward the high-efficiency class, while a negative value pushes it toward the low-efficiency class. The magnitude of the Shapley value indicates the strength of the feature’s influence. SHAP provides both global and local interpretability, which is essential for understanding complex perovskite solar cell fabrication data.
In the SHAP summary, the coating speed was the most influential feature. When the coating speed was high, its SHAP values were mostly negative. This indicates that in my current experimental range, a higher coating speed tends to reduce the probability of obtaining a high-efficiency perovskite solar cell. A moderate or lower coating speed may therefore be beneficial. The dilution volume was the second most influential feature. High dilution volume also tended to have negative SHAP values, which suggests that a highly diluted precursor solution is not favorable for high efficiency. However, extremely low dilution volume may also be unfavorable, because the SHAP values in the positive region were mostly purple, indicating that both excessively high and excessively low dilution volumes can be problematic. The current experimental values of dilution volume may already be close to a reasonable range.
The cleaning annealing time of the self-assembled monolayer showed that shorter times were generally better. The intrinsic passivation concentration showed a more complex pattern. Low passivation concentration did not improve efficiency, while high passivation concentration was also not consistently beneficial. The red points appeared on both sides of the SHAP distribution, which suggests that high passivation concentration introduces instability. Therefore, optimizing the passivation concentration toward a moderate or low range may be a promising direction. The categorical passivation materials MDAI2 and MDABr2 showed smaller SHAP contributions. Their effects likely depend on concentration and interaction with other process parameters. Further optimization of their concentration and usage conditions is required. Table 5 summarizes the SHAP-based interpretation of the key features.
| Feature | SHAP direction | Interpretation for perovskite solar cell optimization |
|---|---|---|
| nP_CS | High values tend to decrease efficiency | Reduce coating speed or use moderate coating speed |
| nP_DV | Extreme values tend to decrease efficiency | Maintain dilution volume in a balanced range |
| nS_CAT | Shorter times tend to increase efficiency | Shorten self-assembled monolayer annealing time |
| nP_IPC | High values are unstable | Explore moderate or low passivation concentration |
| cP_IIsPM_MI | Small contribution | Optimize together with concentration |
| cP_IIsPM_MBr | Small contribution | Optimize together with concentration |
The SHAP analysis revealed that the machine learning model did not simply memorize the training data. Instead, it captured meaningful process-property relationships that are consistent with perovskite solar cell physics. For example, the coating speed affects the nucleation and growth of the perovskite film, which in turn affects grain size, defect density, and carrier lifetime. The dilution volume affects the precursor concentration, which influences supersaturation and crystallization kinetics. The passivation concentration affects surface defect density and nonradiative recombination. The annealing time of the self-assembled monolayer affects substrate surface energy and molecular ordering, which influences perovskite film growth. These physical mechanisms support the validity of the data-driven model.
Experimental Validation Guided by Model Interpretation
Based on the SHAP analysis, I designed a set of validation experiments. I focused on the two most influential continuous features, namely coating speed and intrinsic passivation concentration. I also considered the dilution volume and the self-assembled monolayer annealing time because of their high importance. I kept other features fixed or varied them only within a narrow range to avoid excessive experimental complexity. I did not adjust the self-assembled monolayer annealing time and the MDABr2 passivation material in the first validation round, because the data exploration showed that their current distributions were already reasonable and because the SHAP contributions were relatively small. I systematically varied the coating speed and the intrinsic passivation concentration according to the model recommendation. Table 6 shows the selected experimental conditions and the corresponding predicted efficiency.
| Condition | nP_CS | nP_IPC | nP_DV | nS_CAT | Predicted PCE class | Measured PCE (%) |
|---|---|---|---|---|---|---|
| 1 | Low | Moderate | Medium | Short | High | 20.12 |
| 2 | Moderate | Moderate | Medium | Short | High | 21.81 |
| 3 | Moderate | Low | Medium | Short | High | 20.64 |
| 4 | High | Moderate | Medium | Short | Low | 18.32 |
| 5 | Moderate | High | Medium | Short | Low | 17.95 |
The champion device was obtained under condition 2, with a measured power conversion efficiency of 21.81%. This value is significantly higher than the efficiencies obtained under conventional experimental conditions. The current density-voltage curve of the champion perovskite solar cell showed a high open-circuit voltage, a high short-circuit current density, and a high fill factor. The external quantum efficiency spectrum further confirmed the broad spectral response of the wide-bandgap perovskite solar cell. The integrated current density from the external quantum efficiency spectrum was consistent with the short-circuit current density measured from the current density-voltage curve, which validates the reliability of the measurement.
The experimental validation demonstrates that the machine learning framework can guide the fabrication of high-efficiency perovskite solar cell devices. The model did not merely fit the existing data; it provided actionable recommendations that led to a new record efficiency in my laboratory. The combined use of gradient boosting and SHAP analysis made the optimization process transparent and physically interpretable. The model identified coating speed and passivation concentration as the most promising parameters to adjust, and the experimental results confirmed this prediction.
Discussion of Physical Mechanisms
The coating speed influences the perovskite solar cell performance through several coupled mechanisms. At low coating speed, the solvent evaporation is slower, which can promote grain growth and reduce grain boundary density. However, excessively low coating speed can lead to thick films with increased series resistance. At high coating speed, the film becomes thinner and may suffer from incomplete coverage, pinholes, and poor crystallinity. The optimal coating speed balances light absorption, carrier transport, and defect density. In my experiments, the moderate coating speed gave the best performance, which is consistent with the SHAP analysis that high coating speed tends to reduce efficiency.
The dilution volume affects the precursor concentration. A high dilution volume reduces the concentration, which can slow down nucleation and lead to incomplete film formation. A low dilution volume increases the concentration, which can accelerate nucleation but may also cause rapid crystallization, resulting in small grains and high defect density. The optimal dilution volume provides a supersaturation condition that favors uniform nucleation and controlled grain growth. The SHAP analysis indicated that extreme dilution volumes are unfavorable, which is consistent with classical nucleation and growth theory.
The intrinsic passivation concentration affects surface defect density and nonradiative recombination. Passivation molecules can coordinate with undercoordinated lead or halide ions and reduce deep-level traps. However, excessive passivation can form insulating layers, disrupt charge transport, or create new defects. The SHAP analysis showed that high passivation concentration is unstable, which suggests that a moderate concentration is preferable. This is consistent with the trade-off between defect passivation and charge transport in perovskite solar cell devices.
The self-assembled monolayer annealing time affects substrate surface energy and molecular ordering. A short annealing time may leave residual solvent and disordered molecules, while a long annealing time may cause desorption or degradation. The SHAP analysis indicated that shorter annealing times are generally better within the explored range. This suggests that the self-assembled monolayer can form a sufficiently ordered layer without prolonged annealing, and that excessive annealing may damage the interface.
Limitations and Future Directions
Although the framework achieved promising results, several limitations remain. First, the dataset was collected from a specific laboratory setup and a specific wide-bandgap perovskite solar cell composition. The applicability of the trained model to other perovskite solar cell compositions, device architectures, and fabrication environments is not guaranteed. Future work should validate the framework on multiple datasets and across different laboratories. Transfer learning and domain adaptation could help improve generalization.
Second, the feature selection methods have inherent limitations. Random forest importance can be biased toward features with high cardinality or continuous features. Pearson correlation only captures linear relationships. Recursive feature elimination depends on the model used for evaluation and may be computationally expensive. Future work could explore other feature selection methods, such as permutation importance, mutual information, and regularization-based selection.
Third, the current experimental validation covered only a limited number of predicted conditions. Although the champion device reached 21.81% power conversion efficiency, the full generalization ability of the model has not been comprehensively evaluated. I plan to expand the experimental validation to more predicted conditions and to build a complete closed-loop prediction-validation system. This will strengthen the practical utility of the machine learning framework for perovskite solar cell development.
Fourth, the binary classification approach simplifies the continuous power conversion efficiency landscape. Although classification is useful for identifying high-efficiency conditions, regression models could provide more detailed predictions of the exact efficiency. Future work could combine classification and regression in a multi-task learning framework. The classification model can screen high-efficiency candidates, and the regression model can rank them more precisely.
Fifth, the SHAP analysis provides valuable insights, but it does not establish causality. The correlations between process parameters and efficiency may be confounded by unmeasured variables or hidden interactions. Future work could incorporate causal inference methods and design-of-experiments strategies to validate the causal effects of the recommended process parameters.
Broader Impact on Perovskite Solar Cell Research
The machine learning framework developed in this work has broader implications for perovskite solar cell research. It demonstrates that data-driven optimization can complement traditional physics-based approaches. The framework can be adapted to other perovskite solar cell compositions, such as narrow-bandgap perovskites for bottom cells, mixed-halide perovskites for tandem applications, and lead-free perovskites for sustainable photovoltaics. It can also be extended to other photovoltaic technologies, including organic solar cells, copper indium gallium selenide solar cells, cadmium telluride solar cells, and silicon heterojunction solar cells.
The integration of machine learning with perovskite solar cell fabrication can accelerate the discovery of new process windows, reduce experimental cost, and improve reproducibility. The SHAP analysis provides a transparent way to communicate model decisions to experimentalists. This is particularly important because perovskite solar cell fabrication involves many coupled parameters, and experimentalists need to understand why a particular condition is recommended. The combination of gradient boosting and SHAP is therefore not only a predictive tool but also a knowledge discovery tool.
In my workflow, data quality is as important as model complexity. I invested significant effort in data curation, outlier removal, encoding, normalization, and class balancing. The final model performance depends strongly on these preprocessing steps. I recommend that future studies report their data preprocessing pipelines in detail, including the criteria for outlier removal, the encoding strategy for categorical variables, the normalization method, and the class balancing method. This will improve reproducibility and allow fair comparisons across different machine learning studies for perovskite solar cell development.
Summary of Key Equations and Metrics
For completeness, I summarize the main equations used in this work. The min-max normalization is:
$$ x’ = \frac{x – x_{\min}}{x_{\max} – x_{\min}} $$
The Pearson correlation coefficient is:
$$ r = \frac{\sum_{i=1}^{n}(X_i – \bar{X})(Y_i – \bar{Y})}{\sqrt{\sum_{i=1}^{n}(X_i – \bar{X})^2}\sqrt{\sum_{i=1}^{n}(Y_i – \bar{Y})^2}} $$
The classification metrics are:
$$ \text{Accuracy} = \frac{N_{TP} + N_{TN}}{N_{TP} + N_{TN} + N_{FP} + N_{FN}} $$
$$ \text{Recall} = \frac{N_{TP}}{N_{TP} + N_{FN}} $$
$$ \text{Precision} = \frac{N_{TP}}{N_{TP} + N_{FP}} $$
$$ F1 = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}} $$
$$ \text{AUC} = \frac{1}{N_{pos}N_{neg}} \sum_{i=1}^{N_{pos}} \sum_{j=1}^{N_{neg}} \theta(y_i > y_j) $$
The Shapley value is:
$$ \phi_i = \sum_{S \subseteq N \setminus \{i\}} \frac{|S|!(|N|-|S|-1)!}{|N|!} \left[ f(S \cup \{i\}) – f(S) \right] $$
These equations form the mathematical foundation of the machine learning framework for perovskite solar cell optimization.
Conclusion
I have developed a machine learning-driven framework for accelerating the development of high-efficiency perovskite solar cell devices. The framework includes rigorous data collection, outlier removal, one-hot encoding, min-max normalization, threshold selection, SMOTE-Tomek balancing, random forest feature importance, Pearson correlation filtering, recursive feature elimination, and gradient boosting classification. The gradient boosting model achieved the best overall performance among six machine learning algorithms, with a weighted score of 0.7415. The SHAP analysis identified coating speed, dilution volume, intrinsic passivation concentration, and self-assembled monolayer annealing time as the most influential process parameters. Guided by the model interpretation, I designed and fabricated perovskite solar cell devices with a champion power conversion efficiency of 21.81%. This work demonstrates that machine learning can overcome the limitations of traditional trial-and-error experimentation and can provide actionable, interpretable, and physically meaningful guidance for perovskite solar cell development. The framework is general and can be extended to other perovskite compositions and photovoltaic technologies. It offers a new perspective and scientific basis for the rapid development of high-efficiency perovskite solar cell devices and contributes to the broader goal of sustainable renewable energy.