Fig. 1 presents the workflow employed in this study to predict the crystal structure of lithium manganese silicate cathodes using data sourced from the Materials Project. The dataset consisted of 211 DFT-computed entries containing the selected input features, while the output crystal structure was encoded as a binary label, with 0 representing monoclinic and 1 representing triclinic structures.

The data were divided into 169 training samples and 42 testing samples, and nine ML algorithms were applied to develop predictive models. This 80:20 division follows a widely accepted practice in machine-learning studies, providing a balanced compromise between model training and unbiased evaluation. The split was generated through random partitioning to avoid sampling bias and ensure that the model performance reflects true generalization to unseen data. Model performance was evaluated using multiple assessment metrics including accuracy (ACC), Matthew’s correlation coefficient (MCC), recall (RCC), precision (PRE), F-score (F), negative predictive value (NPV) using Eqs. (6)–(11). Based on overall prediction accuracy, the best-performing model was identified and subsequently subjected to detailed optimization and analysis of its architecture and predictive behavior. (6)ACC =TP+TN(TP+TN+FP+FN) (7)MCC =(TP∗TN−FP∗FN)(TP+FP)∗(TP+FN)∗(TN+FP)∗(TN+FN) (8)Recall (RCC)=TP(TP+FN) (9)Precision (PRE)=TP(TP+FP) (10)F− score (F)=2∗RCC∗PRERCC+PRE (11)NPV =TN(TN+FN)

Here, TP = true positive, TN = true negative, FP = false positve, FN = false negative.

The entire dataset was obtained from the Materials Project Database [9], which provides DFT computed properties of 211 cathode materials with Li-Si-(Mn)-O compositions. All DFT calculations and structural optimizations were performed using the VASP software within the Materials Project framework. The exchange–correlation potentials were treated using the generalized gradient approximation (GGA) or GGA + U, and the DFT energies for the Li-Si-(Mn)-O systems were generated through a high-throughput computational workflow. The initial DFT calculations containing positions of atoms and lattice parameters of crystals can be based on available data from inorganic crystal structure database [27].

The dataset includes the E_f, E_h, E_g, number of sites (N_s), density (ρ), the volume of the unit cell (V), and crystal structure of each electrode. The available dataset is divided into 80:20 as training and testing datasets. To avoid any bias in the training process, each method-based model is trained 100 times, and the models are stored. The data inputs are the chemical formula, space group, E_f (eV) E_h (eV), E_g (eV), N_s, ρ (g.cm⁻³) and V (A³). The output is the crystal structures of Li-Si-(Mn)-O cathode materials that are monoclinic (0) or triclinic (1). Fig. 2 presents the pair plot of the properties of Li-Si-(Mn)-O cathode materials in the dataset. The diagonal elements illustrate the distribution of individual features, while the off-diagonal plots show pairwise relationships between variables. The symmetry along the diagonal reflects similar distributions across parameters, and the axes appear mirrored due to the pairwise plotting arrangement.

No clear correlation is observed between the selected features and the resulting crystal system, highlighting that simple linear or direct relationships are insufficient to describe the underlying structure–property interactions. This lack of explicit trends underscores the necessity of employing advanced modelling techniques capable of capturing complex, nonlinear dependencies within the data. Therefore, ML-based modelling becomes essential for reliably predicting the crystal structures of lithium manganese silicate cathodes, where multiple compositional and structural factors interact in a non-trivial manner.

A comparative assessment of each of the nine ML algorithms was conducted to evaluate their performance using various statistical indicators, including ACC, RCC, PRE, specificity, NPV, and F-score (Table 2). The results revealed substantial variability in the generalization capability of different models. The DT model exhibited good fitting during training (accuracy = 0.887) but demonstrated a sharp decline in testing accuracy (0.639), indicating overfitting. In contrast, the ensemble-based models, RF and XGBoost, showed superior performance, achieving nearly perfect training accuracies (1.000 and 0.993, respectively) and strong testing accuracies (0.803 and 0.721, respectively). Notably, RF outperformed all other models in terms of balanced accuracy, recall, and precision on the test set (accuracy = 0.803, recall = 0.786, precision = 0.917, F-score = 0.846), highlighting its robustness and effective handling of complex nonlinear relationships. The SVM classifier demonstrated moderate predictive ability (testing accuracy = 0.688), providing a stable but not outstanding performance. The Nearest Neighbors Classifier yielded lower testing accuracy (0.606), which may be attributed to its sensitivity to noise and local data variations.

The SGD classifier exhibited the weakest performance across all metrics (testing accuracy = 0.443, F-score = 0.292), indicating poor convergence in nonlinear feature spaces. Among the probabilistic approaches, Gaussian NB and GP classifiers achieved comparable results, with the latter showing slightly higher predictive balance (testing accuracy = 0.705, F-score = 0.757). The ANN achieved perfect training accuracy (1.000) and demonstrated strong generalization on the testing dataset (accuracy = 0.761, F-score = 0.906). Although minor overfitting was observed, the ANN effectively captured intricate nonlinear dependencies, outperforming most conventional algorithms in terms of overall predictive reliability.

These findings suggest the ANN model achieved the highest prediction accuracy and demonstrated the strongest capability to learn the complex, nonlinear interdependencies among the input features. The remaining eight models were optimized using standard and widely accepted hyperparameter-tuning procedures (e.g., grid search, cross-validation, and built-in optimization routines), and their performance showed relatively low sensitivity to tuning variations. Therefore, an extensive architectural explanation was not required for them. In contrast, the ANN contains multiple architecture-dependent parameters such as the number of layers, neurons per layer, activation functions, learning rate, and momentum terms, and its performance was highly sensitive to these choices. To ensure transparency, fairness, and reproducibility, the detailed ANN architecture, optimization strategy, and training behavior will be provided in the coming sections.

Fig. 3 shows the data classed for training and testing data in monoclinic and triclinic crystal structures. In the monoclinic crystal structure, 111 training data and 28 data out of 139 data were investigated, and the training data were not classified, with four of the testing data being unclassified. Also, 58 training data and 14 testing data out of the total 72 data were investigated in the triclinic crystal structure, and the triclinic crystal structure also showed unclassified data in the training data, and the testing data showed unclassified data in six testing data.

The ANN model was trained using the training dataset with systematic optimization of key hyperparameters. The core ANN algorithm was implemented in the C programming language for computational efficiency, while a user-friendly graphical user interface (GUI) was developed in Java to facilitate model execution, parameter adjustment, and visualization of results. The number of hidden layers were varied from 1 to 3, the number of neurons per layer from 1 to 30, the momentum coefficient from 0.1 to 1.0, the learning rate from 0.1 to 1.0, and the number of training iterations from 5000 to 70,000. The corresponding changes in model behavior under these settings are illustrated in Fig. 4. The optimized ANN architecture consists of three hidden layers with fourteen neurons in each layer (Fig. 4a). A momentum value of 0.3 (Fig. 4b), a learning rate of 0.6 (Fig. 4c), and 20,000 training iterations (Fig. 4d) yielded the best performance, achieving a prediction accuracy of 94.31%. Further refinement through iteration tuning demonstrated that the highest accuracy of 95.26% was reached at 20,000 iterations. These results clearly demonstrate the significant impact of hyperparameter selection on the ANN’s ability to accurately predict the crystal system of Li-Mn-Si-O materials.

All data, including the chemical formula, space group, experimental, and ANN predicted crystal structure, are presented in the Table 3. The four unclassified data are monoclinic crystal structures in the experimental crystal system and represent triclinic crystal structures in the ANN model. The six unclassified data represent the triclinic crystal structure in the experimental and the monoclinic crystal structure in the ANN model. The commonality of these is that the Space group is P1.

A confusion matrix between the ANN model and the DFT calculated data predicts all data in the dataset as either positive or negative. This classification produces four outcomes.

TP values are accurate positive predictions, FP values are incorrect positive predictions, TN shows accurate negative predictions, and FN represents incorrect negative predictions. The TP value represents the data number when the ANN model prediction and the DFT prediction are both monoclinic, and the TN values represent the data number when both the ANN model and the DFT prediction are Triclinic. Table 4 shows the evaluation of the confusion matrix. The total data sets are 211. The number of TP, FP, FN, and TN values show 135, 6, 4, and 66. To ensure the reliability of the classification results and to assess the performance of the ANN model, its predictions were compared with the corresponding DFT-calculated data. The model’s performance, evaluated using several statistical metrics, is presented in Fig. 5.

The ACC value of the optimized ANN model was found to be 0.953, indicating a high level of predictive reliability. The MCC, which evaluates the balance between under- and over-predictions—where MCC = 1 represents a perfect prediction and MCC = 0 corresponds to a random assignment—was 0.894, signifying strong consistency between predicted and actual classifications. The precision (PRE), representing the ratio of correctly predicted positive cases to all predicted positives, was 0.957. The F-score, defined as the harmonic mean of precision and recall (ideal value = 1), was 0.963, further confirming the model’s strong performance. The NPV, which measures the ratio of correctly predicted negatives to total predicted negatives, was 0.943, demonstrating that the model effectively distinguishes between the two crystal systems.