Figure 11
A line graph titled Long-term degradation prediction with uncertainty bounds. The horizontal axis is labeled Time (years) and ranges from 0 to 10. The vertical axis is labeled Volume-averaged property retention and ranges from 0.0 to 1.0. The graph features a solid blue line representing the ensemble mean prediction and a shaded blue band indicating the plus or minus 2 sigma uncertainty interval. The ensemble mean prediction line shows a downward trend, indicating a decrease in volume-averaged property retention over time. The shaded band around the line represents the variability across the ensemble, reflecting epistemic variability associated with limited short-term data and highlighting the stabilizing influence of embedded reaction-diffusion and Arrhenius constraints during long-term extrapolation.Long-term (10-year) volume-averaged property-retention prediction obtained using the trained physics-informed digital twin. The solid curve represents the ensemble mean prediction derived from multiple independently initialized PINN models, while the shaded band indicates ±2σ variability across the ensemble. The bounded and smoothly evolving uncertainty envelope reflects epistemic variability associated with limited short-term data and highlights the stabilizing influence of embedded reaction–diffusion and Arrhenius constraints during long-term extrapolation