## 3 Results and Discussion
### The Discussion of the Overall Reconstruction Error and the Hotspot Tracking Performance
However, for _Tfeld3_, the implementation of AGES increases \(\text{Cond}(\mathbf{B})\) to varying degrees, thereby exacerbating the ill-conditioned nature of the problem. Conversely, the reconstruction error still decreases to varying degrees. As shown in Figure 11, AGES demonstrated superior NRMSE reduction capabilities over AHK. This can be attributed to the fact that AGES employs a dual-action strategy, which gives local refinement of grids near identified hotspots and sparse meshing across thermally uniform regions, thereby pre-optimizing \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**coef\({}_{\text{HE}}\)**} & \multicolumn{4}{c}{\(\mathbf{D_{\text{h}}}\)/\%} \\ \cline{2-5}  & **Basis** & **AHK** & **AGES** & **AGES-AHK** \\ \hline
0.1 & 1.41, 1.41 & 1.41, 1.41 & 0, 1.41 & 1.41, 1.41 \\
0.2 & 0.14, 1.41 & 1.41, 1.41 & 1.41, 1.41 & 1.41, 1.41 \\
0.5 & 0, 0 & 0, 0 & 0, 0 & 0, 0 \\
1 & 0, 0 & 0, 0 & 0, 0 & 0, 0 \\ \hline \end{tabular}
\end{table} 
Table 4: The hotspot position deviation of _Tfeld2_. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**coef\({}_{\text{HE}}\)**} & \multicolumn{4}{c}{\(\mathbf{D_{\text{h}}}\)/\%} \\ \cline{2-5}  & **Basis** & **AHK** & **AGES** & **AGES-AHK** \\ \hline
0.1 & 1, 3.16, 6.32 & 1.41, 2, 3.16 & 1.41, 3, 3 & 1.41, 3, 2 \\
0.2 & 3, 2.24, 3.16 & 1, 2.24, 2 & 1.41, 0, 3 & 1.41, 2.41, 1 \\
0.5 & 2.24, 0, 2 & 2.24, 0, 2.24 & 1.41, 0, 1 & 2.24, 0, 1.41 \\
1 & 2, 2, 1.41 & 1.41, 1.41, 1 & 2, 1, 1 & 1.41, 1, 0 \\ \hline \end{tabular}
\end{table} 
Table 5: The hotspot position deviation of _Tfeld3_. grid density distribution to match the temperature field topography. This bidirectional optimization outperforms AHK's unidirectional kernel adjustment in reducing NRMSE. It can thus be concluded that the AGES pre-fits the temperature field from the meshing perspective, thereby facilitating improvement in the reconstruction performance. And this positive effect clearly overwhelms the negative effect of the increased ill-conditioned nature of the problem. The AGES-AHK method implements adaptive kernel adjustments on AGES-optimized nonuniform grids, integrating the optimization of AHK. As shown in Figure 12, AGES-AHK reduces the Cond(**B**) across all temperature phantoms compared to standalone AGES or the basis method. This reduction directly translates to mitigating the ill-conditioned nature of the AP problem, especially in regions with high temperature gradients, thereby effectively reducing the reconstruction difficulty and errors. As shown in Figure 13, the hotspot temperature error \(E_{\text{h}}\) of all four methods exhibits a progressive increase with elevated \(\text{coef}_{\text{HE}}\) values in the three temperature phantoms, indicating an exacerbation of the hotspot peak temperature tracking performance. Once again, the effect of the intrinsic characteristics of the reconstructed temperature field on the difficulty of reconstruction is verified through simulation. A comparative analysis with the basis method reveals that both the AGES and AHK methods effectively reduce \(E_{\text{h}}\) across all three temperature phantoms. Notably, AGES demonstrates superior \(E_{\text{h}}\) reduction compared to the AHK method. This discrepancy arises because the AHK method exclusively reduces Cond(**B**) through kernel function modifications, thereby alleviating the ill-conditioned nature of Equation (10) and enhancing the overall reconstruction accuracy. However, since AHK does not alter the uniform mesh discretization, the inherent limitation of the domain discretization assumption remains unaddressed. The observed \(E_{\text{h}}\) reduction of AHK is a secondary effect of its NRMSE reduction.