# Solid-State Lithium Battery Cycle Life Prediction Using Machine Learning
## 4 Discussion
The forms of the fifth and sixth formulas are more complicated and lose their original physical meaning after calculation. However, it can still be seen that the values of charging/discharging energy and capacity are directly proportional to the _RUL_ and the values of resistance and polarization degree are inversely proportional to the _RUL_. However, these two formulas were abandoned because they did not meet the trade-off between accuracy and complexity. Therefore, the fourth formula, containing features X20 (kurtosis) and X1 (charge-specific capacity), was the best compromise between accuracy and complexity. We further investigated the fourth formula in Table 2 by comparing the predicted _RUL_ and the true value of all experimental cycles. As shown in Figure 7, the upper-right corner of the plot demonstrates the initial stage of battery cycling. At this stage, the predicted value was less than the actual value. This might be due to the absence of significant aging characteristics, and the model could not accurately predict the battery life from the selected features. The lower-left corner of the plot shows the end stage of the battery cycling, and the predicted value was slightly higher than the actual value at this time, which may have been caused by the rapid decline in various performance indicators [31]. In the middle of the chart, the accuracy of the model was the most satisfactory. The obvious aging characteristics shown by the batteries are convenient for the model to capture and predict. Basically, all the data points were concentrated on the diagonal of the pair plot, which shows that the predicted value was in good agreement with the actual value. Our model achieved an excellent prediction accuracy from the perspective of R\({}^{2}\) (0.91) and RMSE (18.17). Through appropriate pretraining on LFP solid battery data, the model also exhibited a passable transfer prediction ability for NMC solid battery data. These experimental results showed that the method developed in this paper is universal in the field of solid-state lithium batteries with different material systems. Then, we compared our results with the other three methods, SVR, GPR, and elastic net, in Table 3. SVR is a nonparametric algorithm based on support vector machine, GPR is a kernel-based probabilistic model that predicts according to the similarity between samples, and elastic net is a regularized linear regression model. These three methods have been employed frequently in the recent literature, and they have achieved high accuracy. However, due to the existence of an internal fixed formula, they still have no satisfactory adaptability and applicability in different battery systems. For accuracy comparison during these machine-learning models, we randomly selected cycles 53, 105 and 179 as examples. As the number of cycles increased, the advantage of our model gradually became obvious. At cycle 179, the predicted _RUL_ error led by SR reduced to 0, while the predicted _RUL_ errors of SVR, GPR, and EN remained high at 27, 13, and 27, respectively. R\({}^{2}\) and RMSE were evaluated by comparison between the prediction _RUL_ values of four methods and the true _RUL_ values from whole cycles of the test battery. The higher prediction accuracy of our SR model was attributed to the screened features, which accurately tracked the battery degradation and created highly correlated inputs for the SR model. The diversity of applied symbols broke the restriction of fixed expressions and was also helpful for better optimization results [41]. However, the computation cost might be the current limitation of this model, as listed in Table 4. Comparing the other three methods with the fixed mapping formula form, the training time and storage consumption of symbolic regression were larger. This can be improved by reducing the number of screened features and formula symbols using domain knowledge in future work. Besides, the training process is strongly dependent on the quality and quantity of battery testing data.