## 4 Conclusions  
In this research, a novel reconstruction method for acoustic pyrometry dedicated for strong temperature gradients and limited measurement points is proposed and demonstrated. Based on the qualitative and quantitative analyses of the reconstruction results, the following conclusions can be drawn:  
1. The effect of the intrinsic characteristics of the reconstructed temperature field (\(C_{\text{HE}}\)) on the difficulty of reconstruction is verified through literature reviews and reconstruction results.
2. The finalized adaptive hybrid kernel from the AHK method combines the sharp spatial localization characteristics of G with the global characterization of MQ, thereby alleviating the ill-conditioned nature of the problem and enhancing the suitability for reconstructing large-gradient temperature fields.
3. By implementing adaptive nonuniform meshing without increasing the total grid number, AGES pre-optimizes grid density distribution to match the temperature field topography, thereby facilitating improvement in the reconstruction performance.
4. The finalized AGES-AHK method integrates the optimization of AHK and AGES, achieving significant improvements over basis data in both reconstruction fidelity and hotspot characterization. At \(C_{\text{HE}}\) levels below 15, the AGES-AHK method achieved the lowest NRMSE of less than 3.7%, \(E_{\text{h}}\) of less than 15% and \(D_{\text{h}}\) of less than 2.24%, representing its superior overall reconstruction performance and hotspot tracking ability. Even at the highest \(C_{\text{HE}}\) level of 30, the AGES-AHK method was still able to reproduce the overall temperature field topography and qualitatively track the hotspots.  
These conclusions have important implications for furnace temperature monitoring, combustion control, environmental protection and energy saving. One promising direction is the further improvement of discretization methods, particularly for highly irregular temperature fields. Exploring alternative mesh refinement techniques and hybrid kernel functions, such as incorporating the use of machine learning-based predictions of temperature gradients, could enhance grid evolution strategies and flexible kernel functions. Additionally, implementing noise reduction techniques and regularization techniques in the reconstruction process could help improve the reconstruction robustness. Furthermore, incorporating additional information or constraints in combination with our proposed methodology could further improve reconstruction performance under extreme conditions. These advancements would enable more widespread application of the AGES-AHK method in industrial settings for better prospects.  
**Author Contributions:** J.T.: conceptualization, methodology, validation, software, writing--original draft preparation. L.C.: writing--original draft preparation, visualization. N.L.: supervision, project administration, funding acquisition, writing--review and editing. Q.Z.: conceptualization, supervision, formal analysis. Z.G.: visualization, supervision, funding acquisition. J.Z.: resources, funding acquisition, investigation, data curation. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Key Laboratory of Aerospace Liquid Propulsion Fund (No. HTKJ2023 KL011007).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article[PERSON] Further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest[PERSON]