# Machine Learning Based Surrogate Models for the Thermal Behavior of Multi-Plate Clutches
## 4 Discussion  
Considering the magnitude of the RMSE values (between 4.29 and 28.22) in relation to the magnitude of the output variable (temperature ranging between 350 K and 1000 K), none of the five models considered turned out to be completely unsuitable regarding temperature predictions based on the axial force and the rotational speed. This outcome was also confirmed by the MAPE scores. Average absolute deviations of no more than 4.02% were achieved in all models in both use cases. Nevertheless, both the GP and BPNN stood out as the best alternatives for the surrogate models. The disadvantages of these two models was a significantly higher level of complexity than the PR, DT, and SVR, as well as the greater training time. Furthermore, all the models met the requirement of providing nearly real-time temperature predictions during operation. The inference times obtained were negligible compared to the simulation time and the duration of the switching process. The PR model, which is characterized by its simplicity, also achieved acceptable results in the first use case. In the second use case, which also considered the variation of the lining thickness during operation, the GP and the BPNN provided the best results. The PR models, which competed with the two best models (GP and BPNN) in Use Case 1, demonstrated significantly worse performance in this case.  
Suppose not only the RMSE and MAPE scores, which indicate the average performance of the models, are taken into account, but individual slip cycles are analyzed as well. In that case, the SVR can be directly discarded as a good surrogate model. In both use cases, the SVR did not manage to reproduce the oscillations due to the three slip cycles in the temperature profile and only mapped the basic increase in temperature. Regarding Use Case 2, all but the DT and BPNN models exhibited the behavior of the SVR model in the first use case and they demonstrated weaknesses in replicating the fluctuations of the temperatures. It is also important to mention that Figures 9 and 13 show only individual slip cycles as examples and that these results cannot be applied to all other slip cycles.  
Regarding the research on the influence of data volume, both use cases showed that an increase in data volume fundamentally leads to improved performance. The range between 80 and 100 simulations can be considered preferable. In the two best models (GP and BPNN) an acceptable performance was reached within this range, with still manageable quantities of data to be generated. Larger data volumes achieved better results, but the improvement was not substantial.  
In future work, we plan to extend the models to include more variables. For instance, the maximum temperature can be predicted in addition to the temperature of the material at any given x and y coordinates. Other geometry (steel plate thickness) and material parameters (Young's modulus, heat capacity, etc.) or initial temperature distribution and oil temperature can also be taken into account. Based on these extended surrogate models, a sensitivity analysis can also be performed in order to further investigate the influences of the individual parameters on temperature behavior. Furthermore, other approaches such as physics-informed neural networks can be considered, which utilize not only the data, but also the existing physical knowledge about the domain to generate the models.