Figure 4
The horizontal axis is labeled “Operational time”, ranging from 0.0 to 1.0 with an interval of 0.2. The vertical axis is labeled “Sustainability state tau”, ranging from 0.0 to 0.8 with an interval of 0.2. Two curves are plotted and identified in a legend at the upper left: a solid blue line labeled “Physical aging” and a dashed orange line labeled “Digital twin (mean, 5-fold)”. The blue curve starts at (0, 0.0) and increases steadily, showing a gradual rise in sustainability state, reaching 0.9 at time 1.0. The orange dashed curve starts higher at about (0, 0.4) and increases more rapidly, remaining above the blue curve throughout the entire range. It approaches saturation near 0.93 by time 1.0. Note: All numerical values are approximated.Comparison between the analytical physical aging trajectory and the mean sustainability state predicted by the physics-informed digital twin across five-fold cross-validation. The close agreement and smooth, bounded evolution of the predicted state demonstrate physically admissible, monotonic behavior with asymptotic convergence governed by the imposed irreversible kinetics