## 5 Results
It is also important to note that model analysis was performed on the global pumping system, which includes data from both NCP1A and NCP1B pumps. Models of each individual system were also generated to establish differences. The next block concerns the assessment of the models. Although there are different model performance measures, an excellent way to measure a model's performance and compare its accuracy with that of different models is by using the Mean Square Error (MSE) [64]. Therefore, the model that develops a lower MSE after training in the training set is the one with greater accuracy. A model performance summary is presented in Table 1, showing that the accuracy of the regularized models is better than that of the simple linear model. This fact may imply that this model tends to overfit the data. Concerning non-linear models, both the decision tree and random forest models performed much better than the K-nearest neighbor algorithm. In particular, random forest has the highest prediction among the nonlinear models [70]. Although the MSE value for the random forest algorithm is very similar to that of the regularized ElasticNet algorithm, the latter has a significantly lower standard deviation of the MSE values. Therefore, we selected ElasticNet for prediction [71]. Figure 5: Structure of the dataset. (**a**) Color-encoded correlations between process variables. (**b**) Histogram of the targeted variables. Since the random forest method is nothing more than a bagging ensemble method, other ensemble methods perform similarly, as presented in Table 2.  
Models with better results were optimized using the Scikit-Learn library. The optimization process consisted of selecting the best hyperparameters for the model adopted with respect to the entire training dataset for the pumping system by using a grid search. Two hyperparameters were optimized for the ElasticNet model. The first represents the degree of regularization. The higher the value of \(\alpha\), the greater the penalty for the weighted terms and the greater the degree of regularization. The second parameter refers to the type of regularization, denoted as L\({}_{1}\) regularization (Lasso) when its value is 1, and L\({}_{2}\) regularization (Ridge) when its value is 0. The MSE value was reduced, and the optimized value for both hyperparameters was found to be 0.5, producing an MSE value of 17.14 for the NCP1A pump. The benefits of the NCP1B pump are slightly short of the target, with an MSE of 20.22. All the experiments were conducted on a Linux workstation equipped with 32 GB of system RAM and an NVIDIA Quadro GPU with 24 GB of VRAM. Implementation was carried out in Python 3.10, employing deep learning models that use CUDA version 12.4 for GPU acceleration. The average training time in cross-validation folds was approximately 5 min and 17 s, with a standard deviation of 1 min and 23 s. This demonstrates the computational feasibility of the framework for near-real-time adaptation or retraining scenarios, especially in industrial environments where hardware acceleration is available. Regarding research question RQ1 posed in Section 1, after the analysis was carried out, it became evident that multiple models can be involved in estimating the desired parameter. This includes ensemble techniques, such as bagging approaches, as a notable example. To improve the robustness of temperature prediction, a greedy ensemble learning approach that integrates the outputs of several base regression models was used. The integration mechanism is a weighted average, where the weights are determined through a greedy selection process based on validation performance. Specifically, models are ranked by their individual performance in regard to a holdout validation set, and weights are assigned proportionally to the inverse MSE, ensuring that models with better generalization contribute more to the final prediction. In this use case, cooperation between the Lasso, ElasticNet, and RandomForest models was employed, and the final performance is summarized in Table 3.