Figure 7
Two graphs depict error analysis and PDE residual. Panel A contains two graphs: a histogram and a QQ-plot. The histogram shows the distribution of prediction residuals with the horizontal axis labeled P pred - P meas ranging from -0.010 to 0.020 and the vertical axis labeled count ranging from 0 to 50. The QQ-plot compares ordered values against theoretical quantiles, with the horizontal axis labeled Theoretical quantiles ranging from -3 to 3 and the vertical axis labeled Ordered Values ranging from -0.010 to 0.020. Panel B is a heatmap showing the absolute PDE residual across the time-depth domain. The horizontal axis is labeled Time (days) ranging from 0 to 175, and the vertical axis is labeled Depth (mm) ranging from 0 to 0.5. The color scale on the right indicates the magnitude of the PDE residual, ranging from 0.5 to 3.5.(a) Error histogram and QQ-plot of the prediction residuals, showing a near-Gaussian distribution and good agreement with theoretical quantiles. (b) Absolute PDE residual across the time–depth domain, demonstrating that the PINN satisfies the reaction–diffusion equation with only localized peaks near early-time and boundary regions