Fig. 4: Comparative analysis of model predictions and its uncertainty and calibration for Q_dis in cylindrical sample cells.

Analytical comparison for Q_dis for two datasets; D_NMC+NCA (Panel I) and D_LCO (Panel II), where a depicts the relationship between predicted and actual values of Q_dis, with the diagonal dashed line indicating perfect prediction accuracy, b illustrates the density distributions of predicted versus actual Q_dis. The calibration plot in c assumes a normal distribution, where the mean and standard deviation are estimated from the 10th, 50th, and 90th percentiles of predictions. It depicts the cumulative proportion of actual Q_dis values that fall at or below the predicted quantile values rather than within symmetric intervals around the predictions. The ideal diagonal line represents perfect calibration with the shaded area indicating the degree of miscalibration, denoted A. The approximately diagonal trend of the calibration line up to the 0.5 quantile shows that data with residuals below the median are well described by the predictive distribution. The jump from 0.5 to 1 indicates that the predictive distribution extends further to positive values than the observed distribution of residuals; almost all test data are already covered by the predicted 0.6 quantiles for both datasets. However, the overall miscalibration areas for both datasets are quite similar, indicating that despite different patterns of over- and underconfidence at specific quantiles, the general calibration performance across both datasets is comparable. Box plots at d show the prediction intervals over multiple cycles, demonstrating the median and variability of the model prediction uncertainty over the battery’s lifespan. e provides histograms that depict the quantile-based prediction interval width between the 10th and 90th percentiles as a measure of sharpness. The red dashed line indicates the sharpness as the mean interval width and shows the concentration of the predictive distributions that indicate narrower distribution and, consequently, higher confidence in predicting Q_dis for D_NMC+NCA in Panel I. Further comparisons are in Supplementary Figs. 7, 8, 10, and 12.