Figure 5
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. Six curves are shown and identified in a legend at the lower right: five colored lines labeled “Fold 1” through “Fold 5”, and a solid black line labeled “Physical aging”. The “Physical aging” curve starts at (0, 0.0) and increases steadily, showing a gradual rise in sustainability state, reaching approximately 0.9 by time 1.0. The five fold curves all start higher, around (0, 0.27 to 0.45), and increase more rapidly than the physical aging curve. They remain above the physical aging curve throughout the range and gradually converge toward similar values near 0.92 to 0.93 by time 1.0. Among the folds, most curves closely overlap, while one curve (Fold 4) starts slightly lower near 0.27 and rises more gradually before aligning with the others at higher times. Note: All numerical values are approximated.Five-fold cross-validation consistency of the physics-informed digital twin, illustrating fold-independent sustainability state trajectories. The close overlap across folds indicates that the learned state evolution is governed primarily by embedded physical constraints rather than sensitivity to data partitioning