4.3.1. Effectiveness Analysis of EMM

To measure the EMM's contribution, we designed a variant model without EMM, as described in Table 5: MTPHNet-B. It can be seen that the prediction effect of MPTHNet-A without EMM is extremely poor; it cannot even predict the temperature. The quantitative results show that the EMM is the core of temperature prediction.

### 4.3.2. Effectiveness Analysis of PCEM

We believe the use of PCEM would further improve the accuracy of temperature prediction. To substantiate it, we designed a variant without the PCEM: MTPHNet-C. In Table 5, MTPHNet-A outperforms MTPHNet-C in all metrics. The quantitative results clearly show that PCEM improved the prediction performance.

#### 4.3.3. Effectiveness Analysis of DFM

DFM fuses the features extracted from meteorological and thermophysical parameters, which is a crucial step. To confirm this, we designed a variant model, MTPHNet-D, which replaces the DFM with an additive fusion module. In Table 5, MTPHNet-A outperforms MTPHNet-D in all metrics, and MTPHNet-D is closer to MTPHNet-C in terms of metrics. The quantitative results show that DFM and PCEM contribute similarly to improve the prediction performance.

#### **5. Conclusions**

This study comprehensively considered the thermophysical and meteorological parameters affecting the temperature field distribution of a 3D target. Combined with temperature field distribution data, an intelligent temperature field prediction model, MTPHNet, was proposed. To fuse meteorological and thermophysical parameters, MTPHNet used PCEM to calculate the interaction between 3D target attributes and extract thermophysical features. Simultaneously, it used EMM to map meteorological parameters to meteorological features so that the mapped data and thermophysical data would be of the same size, which facilitated the subsequent data fusion. Finally, DFM fused the parts and used the results to predict the temperature. Considering PCEM's tendency of memory explosion when processing point cloud attribute data, we introduced PointNet as a feature extraction network to reduce the memory burden and divide the feature extraction process into local feature and global feature extraction activities to further streamline memory use. Compared with v-SVR and CBPNN, the MAE and RMSE of MTPHNet were reduced by at least 23.4% and 27.7%, respectively, whereas the R2 value increased by at least 5.85%. The results show that MTPHNet effectively improves model generalizability to more efficiently and accurately predict temperature fields while meeting real-time infrared simulation processing requirements. In complex object temperature field prediction tasks that simulate real environments, MTPHNet is advantageous in that it considers realistic energy interaction processes. Its MAE, RMSE, and R2 values were 2.645, 3.522, and 0.964, respectively, demonstrating the model's high adaptability to real scenes.

It should be noted that when MTPHNet performs multi-model prediction tasks, the number of point clouds of different 3D models are required to be the same, which significantly increases the difficulty of data collection. Therefore, in a future work, we plan to change the model structure so that it can be further adapted to 3D models varying numbers of point clouds.

**Author Contributions:** Conceptualization, Y.C. and L.L.; Data curation, Y.C., B.L., W.Z. and Q.X.; Formal analysis, L.L., W.Z. and Q.X.; Investigation, Y.C.; Methodology, Y.C., L.L. and B.L.; Project administration, L.L. and W.N.; Software, Y.C., W.N. and B.L.; Supervision, L.L. and W.N.; Validation, W.N., W.Z. and Q.X.; Visualization, Y.C. and W.Z.; Writing—Original draft, Y.C. and L.L.; Writing—Review and editing, Y.C. and L.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.

**Conflicts of Interest:** The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

### **References**

