# Model Predictive Evolutionary Temperature Control via Neural-Network-Based Digital Twins
## 3 Results
### Model Predictive Controller Performance  
After validating the accuracy of the digital twin model, the performance of the control law population is investigated via following the experimental protocol described in Appendices B and C. The metrics used to evaluate the controller's performance are the same as the loss functions defined in Equation (2).  
Figure 7: Capabilities of the digital twin model for extrapolation of the fan settings. (**a**) Prediction: Fans [0, 40, 60]; Fans on [100, 100, 100]. (**b**) Prediction: Fans [0, 40, 40]; Fans on [100, 100, 100]. (**c**) Prediction: Fans [60, 20, 20]; Fans off [0, 0, 0]. (**d**) Prediction: Fans [80, 0, 40]; Fans off [0, 0, 0].  
The greatest advantage of the intelligent controller is that it can leverage the speed of the NN-based predictive model to select the best control law policy among the alternatives for the current state trajectory in real time. Figure 8 portrays the change in the temperature field caused by a significant and sudden increase in the thermal load applied to the system, while Figure 9 shows the temporal evolution of performance metrics. In all GP-based tests, a control law population of 10 is deployed. In both figures, the term \"Specialist\" denotes a subset of controls particularly trained to handle high load disturbances. \"General\" refers to control laws learned for the entire operating range. The category labeled as \"Random\" corresponds to the benchmark case, where fan settings are randomly assigned (for further details, refer to Appendix C). It is clearly observed in Figure 9 that both GP controllers (Specialist, General) significantly outperform the random controller. Interestingly, the General population achieves a reasonably similar performance to the Specialist at significantly lower energy consumption.  
When the the heat load is raised to medium range from low loads (Figure 10), the Specialist population was found to outperform both the General control law population and the Random cooling, despite the fact that the fan load of the Random case is much higher (Figure 11). If just the fan settings are considered, Specialist MPC is at a disadvantage to eliminate the hot spots on the surface, compared to the random controller. Yet it was found  
Figure 8: From left to right—Evolution of the temperature field during the experiment: Specialist (**top** row), General (**middle** row) and Random Control (**bottom** row).  
Figure 9: Performance metrics of MPC with 10 individuals at high thermal loads. The x-axis denotes the time, while the y-axis shows the metric.  
in repeated experiments that Specialist population-based control outperforms the others with less power usage for the fans. The performances of the GP-based controller were also tested in the settings where the heat load is reduced (Figures 12 and 13). As expected, the Specialist population is the best performer. However, its energy consumption is also higher. A possible explanation is that since a homogeneous temperature field is currently prioritized over efficiency, individuals that perform better on the hot-spot and standard deviation metrics are overtaken, albeit at a higher energetic cost.  
Figure 11: Performance metrics of MPC with 10 individuals at medium thermal loads. The x-axis denotes the time, while the y-axis shows the metric.  
Figure 12: From left to right—Evolution of the temperature field during the experiment: Specialist (**top** row), General (**middle** row) and Random Control (**bottom** row).