## 5 Simulation and Results of Cardiovascular Disease Prediction
### Validation of Deep Vanilla Recurrent Network for Cardiovascular Disease Prediction  
The results show that DVR-Net outperforms the base models with an accuracy of 91%, F1-score of 90%, recall of 90%, and precision of 91%, as shown in Table 11. When compared to DNN (about 81.5%) and VRNN (about 83.8%) DVR-Net achieves higher accuracy (about 90.5%) and F1-scores for the former. This suggests that DVR-Net offers a better trade-off between recall and precision and is more accurately able to predict CVD. DNN is unable to capture sequential dependencies; its accuracy and F1-score are comparatively lower. This lessens its efficacy when working with complex datasets that exhibit temporal relationships, like data from health indicators, where prediction relies heavily on sequential trends. DNN is computationally expensive and requires specialized hardware to train large datasets. With a recall rate of up to 92%, VRNN outperforms DNN, indicating its superiority in detecting positive cases (heart disease patients). Nevertheless, it has a lower precision (about 79-80%), which means there are more false positives. The overall F1-score and accuracy are impacted by this imbalance. At the time of compilation of DVR-Net, the 'Adam' optimizer is used along with 'loss function'. DVR-Net is trained and the final output is generated. Architecture details for baseline models and DVR-Net is shown in Table 12. The hyperparameters used in individual model and DVR-Net model are shown in Table 13. The Stochastic Gradient Descent (SGD) optimizer is used, as it performs better by reducing fluctuations and greatly accelerating convergence [47]. Tables 14-16 show the results of 10-FCV for DVR-Net with 10, 20, and 30 epochs. The findings demonstrate that, with an accuracy of 91%, our DVR-Net model performs better than the base models. Figure 7 show the different metrics of individual models and DVR-Net. Figure 4 shows that the execution time of both DB-Net and DVR-Net is higher than the individual models. DVR-Net has a substantially longer execution time (training and inference) than DNN and VRNN. While DNN and VRNN are significantly faster, taking only about 742 and 2393 s, respectively, DVR-Net, for instance, can take up to 8712 s to train for 30 epochs. The DVR-Net model complexity, which processes data using both recurrent layers and dense layers, is the cause of this longer execution time. The parameters in DVR-Net have some redundancy because it contains both dense and recurrent layers. In comparison to a single architecture like DNN or VRNN, the model requires twice as much memory because it must store the weights and biases for both the dense and recurrent components. DVR-Net also monitors the intermediate activations from both the dense and recurrent paths during inference and training. Because the model must store activations from two distinct architectures for backpropagation and gradient updates, this further raises the memory requirement. The confusion matrix for DVR-Net is shown in this Figure 8, which summarizes the classification performance of the model by displaying the counts of FP, FN, TP, and TN. DVR-Net successfully detects both positive cases (patients with CVD) and negative cases (healthy individuals) with few misclassifications, as indicated by high values in the TP and TN cells. This balanced accuracy shows how well DVR-Net can differentiate between the two dataset classes. The AUC score in Figure 9 depicts the ROC curve, which indicates how well the model discriminates. A commonly used metric to assess the models ability to distinguish between positive and negative classes across a range of thresholds is the ROC-AUC. Figure 9 illustrates a high level of accuracy with an AUC near 1.0, suggesting that DVR-Net does a great job of differentiating between people who are healthy and those who are at risk of CVD.