# Model Predictive Evolutionary Temperature Control via Neural-Network-Based Digital Twins
## Appendix C MPC Experiment Design  
The next step is to transfer the controller from the virtual to the physical domain and assess its performance on the experimental setup. Figure 14 depicts the final procedure for the MPC experiments with one, or multiple control models.  
Figure A1: The training pipeline for the GP controller.  
More tests were conducted using three distinct control policies: (i) specialist control models based on heat loading, (ii) general-purpose control models, and (iii) a simple control model utilized as a benchmark. The specialist groups were formed by selecting the top 10 performers from the final population in experiments with low (total load \(<\) 100), medium (100 \(<\) total load \(<\) 200), and high heat load conditions (200 \(<\) total load \(<\) 300). As a result, three specialist populations were created, each corresponding to one of the heating load groups. The general group consisted of randomly chosen individuals from the final population.  
To ensure a proper evaluation of the controller's performance, it is essential to maintain comparability among experiments within each group. To achieve this, a standardized workflow is followed, as depicted in Figure 11. The workflow includes the following steps:  
1. Cooling to the initial state: All experiments begin from the same starting point by cooling the system to the initial state. This step ensures consistency across experiments.
2. Recreating a predetermined steady state: To simulate the control of a dynamic system and replicate a realistic scenario, the system is preheated to a predetermined secondary steady state. This step further enhances the reliability of the evaluation.
3. Fixed experiment duration: Each experiment is conducted for a fixed duration of 5 min, with a frame captured every 30 s. This extended monitoring period allows for a comprehensive observation of the evolution of the temperature field. In the MPC tests, three different thermal load scenarios are investigated:  
* High heat loading: the load on the heating strips was suddenly increased from [50%, 25% and 0%] to [75%, 100% and 75%], while the fans were open at [20%, 40% and 20%]. The benchmark control law resulted in a fan setting for the cooling experiment of [70%, 0% and 20%] after the set point change.  
* Medium heat loading: the heating strip loads were suddenly raised from [25%, 0% and 50%] to [25%, 50% and 70%], while the fans were open at [30%, 20% and 30%] during the second steady state. In this situation, the benchmark control law adjusted the fan settings to [30%, 80% and 100%].
* Low heat loading: the thermal load was abruptly reduced from [75%, 75% and 50%] to [0%, 25% and 25%], while the fans were open at [50%, 80% and 0%]. In this case, the benchmark controller set the fan settings to [80%, 50% and 40%].  
Finally, the number of candidates to be evaluated in real-time before applying the control laws needs to be determined. Given our objective of achieving quick response times, it is crucial to strike a balance between evaluation accuracy and computational efficiency. To address this, we employ two different strategies, as illustrated in Figure A2. In the first strategy, a single individual is evaluated. For the specialist populations, the best individual is selected, while for the general populations, a single individual is randomly chosen. This approach ensures a focused evaluation while minimizing computational overhead. In the second strategy, ten individuals are selected for real-time evaluation. Similar to the first strategy, individuals are randomly chosen from the general populations. However, for the specialist populations, the entire population is included in the evaluation. This expanded evaluation allows for a more comprehensive assessment of the control laws. Regardless of the chosen strategy, the randomly generated fan settings remain constant throughout the entire duration of the control experiment. This ensures consistency and eliminates any potential bias introduced by varying fan settings.