# Model Predictive Evolutionary Temperature Control via Neural-Network-Based Digital Twins
## 3 Results  
### Testing Digital Twin as a Predictive Model  
Before implementing with the GP-based controller on the real experimental setup, the performance of the digital twin is first assessed in two distinct aspects. First, it should be able to accurately predict the next two frames given a certain set of inputs. Second, it should be able to capture the impact of the fan loads on the temperature distribution within a virtual experiment, even if it is not part of its training set. In other words, the learnt model representation of the problem in NN parameters should be able to answer \"what if\" questions in a reasonable way. Figures 5 and 6 illustrate some good and bad predictions of the digital twin model on new test experiments with pre-set heat load changes and fan settings. It is worth note here that the digital twin typically performed well for experiment trajectories with around 10 snapshots, while failing to capture the extreme hot spots in very short experiments, which were underrepresented in the training set (see Table 1). For instance, the first experiment in Figure 6 consists of only one executable sequence. As a result, the model never received information regarding the new heat load on the system. Consequently, the prediction is an informed guess, based on the last steady state reached. Similar behavior can be observed in the first predictions for experiments (a) and (b) in Figure 5. Hence, weaker performance is to be expected in such cases. This indicates that input sequences containing only the frames, depicting the steady state reached from the previous experiment, may have a negative influence on the model's predictive capabilities on hot spot risk estimation. Fortunately, we do not parse two consecutive steady-state frames as input to the controller, thus mitigating the effect of such outliers when we evaluate the MPC performance. The reason for the inaccurate predictions for the second experiment in Figure 6 is not clearly identifiable. While it manages to capture the structural evolution of the temperature field, it misses the hot spot formation. One reasonable explanation for this is the effect of sampling through a sparsely populated set of fan settings. Increasing the number of training and validation examples and sampling from a set with smaller intervals may remedy this behavior. In either case, however, the MAPE score was less than 5%, which would still be relatively informative enough to decide upon the best MPC policy given the input sequence. Figure 5: Examples of successful digital twin predictions. GT refers to the ground truth (i.e., experiments). (**a**) Fans [0, 40, 60]; Heating Strips [75, 0, 25]. (**b**) Fans [0, 40, 40]; Heating Strips [75, 100, 100]. (**c**) Fans [60, 80, 100]; Heating Strips [75, 75, 100]. The second assessment for the digital twin is related to its ability to capture the physical relationship between the fan settings and the evolution of the temperature field, as \"understanding\" the fans' impact is crucial for the performance of the controller. For that purpose, we conducted a set of parametric analysis. Given a sequence of inputs, the digital twin first makes a prediction of the next one minute for a given fan setting (e.g., [0%, 40%, 60%]), for which the ground truth measurements exist. After checking model accuracy (MAPE < 2%), the DT is used to estimate how the temperature field would be if the fans were fully open ([100%, 100%, 100%]), or fully closed ([0%, 0%, 0%]). Some examples of the DT predictions are shown in Figure 7. While it is difficult to judge the extent to which the model perceives the impact of cooling on the temperature field distribution, one may conclude that it adequately shifts the prediction with changing fan loads. If they are fully opened, there is an increased cooling effect, while turning the fans off leads to the emergence of some hot spots.