# Application of Machine Learning for Bulbous Bow Optimization Design and Ship Resistance Prediction
## 4 Discussion
In contrast, the GWO algorithm includes these parameters as well as various classes of gray wolf populations, each associated with distinct convergence factors, resulting in a convergence speed surpassed only by the ABC algorithm. In this study, the NURBS surface control points are used to model the bulbous bow, allowing for more localized modifications to the shape of the bow compared to using parameters such as radius, volume, and cross-sectional area. Ideally, each control point on the surface should be treated as an independent input parameter; however, an infinite number of control points would lead to the high-dimensional fitting problem in the surrogate model. Therefore, in this experiment, the overall coordinates of five sets of control points are selected as the input parameters for the model. In future work, the parametric representation of the curve can help reduce the dimensionality requirements to some extent. The prediction results of the CBR model for optimization are generally consistent with those from the CFD simulations, although minor discrepancies still exist. The difference in the underlying principles between the two methods may be the cause of this discrepancy. CFD simulations model the interaction of the fluid with the ship's surface to obtain resistance, dividing the hull into a large number of fine meshes to capture the mechanical characteristics of the fluid, which makes the results of CFD simulations very accurate. In contrast, the CBR model establishes a mapping relationship between hull parameters and ship resistance based on training data and constructs a specific mathematical model to predict ship resistance. Therefore, compared with CFD simulations, the CBR model tends to focus more on the overall trend for more complex nonlinear issues, with differences in detail. Training data are usually derived from CFD simulation results, and in practical scenarios, it is difficult to obtain resistance responses for all possible combinations of ship parameters. However, the CBR model offers significant advantages in terms of computational costs and time requirements. CFD simulations typically involve large computational loads, requiring substantial resources and time, whereas the CBR model allows for rapid predictions, thus improving production efficiency in practical engineering. For example, in this study, the CFD method takes up to 6 h to compute the results for a single sample. Ref. [16] also mentioned that using the viscous flow solver to solve the total resistance coefficient requires 175,000 s. In contrast, the CBR model offers significant advantages in computational cost and time, typically requiring only a few tens of seconds for iteration. This helps improve production efficiency in practical engineering applications. Although there are differences between the CBR model and CFD simulations, when the error requirements are met, this can be viewed as a trade-off between accuracy and speed. This study examined the impact of bulbous bow design on resistance under ideal conditions. Excessively low resistance may indicate a non-traditional hull shape, which could adversely affect the ship's seaworthiness and stability. When designing the hull, it is necessary to consider the balance between resistance and the economic efficiency of the ship. During navigation, environmental factors such as wind and sea waves also influence the total resistance of the hull, particularly during high-speed sailing, where these factors introduce additional constraints in resistance calculations. Consequently, predicting ship resistance under multiple constraints, along with multi-objective optimization of resistance and other performance metrics, is a promising direction for future research.