## 2 Methods and Materials
### Baseline Ship Performance Model  
Before presenting the mathematical formulation and our methodological workflow, it is crucial to introduce the method that will serve as the baseline for our models. The most common and well-established approach for ship performance modelling used in the shipping industry is the combination of sea trial curves with theoretical formulas, such as [PERSON]'s method [41] or ISO-15016 [42]. This approach overcomes the limitations of using sea trial curves regarding changing factors, such as weather conditions, as it accounts for the added resistance due to wind, waves, and currents. It also significantly improves accuracy compared to uncorrected sea trial curves. Moreover, such a method has limited complexity and low computational cost, a crucial criterion for the industry, as it enables its use on vessels with limited resources as the ship performance model for operational optimisations.  
At the Angelicoussis Group, a variation of this approach is used as the ship performance model. The sea trial curves for the group of sister vessels under examination are processed and refined following internal experimentation conducted by the Energy Efficient Department delivering the Power Model illustrated in Figure 1, which estimates the expected generated _Shaft Power_ from the ship's engine with respect to draft and vessel speed under ideal scenarios, such as a clean hull and calm water.  
To accommodate for the fouling (i.e., the accumulation and growth of marine plants on the submerged structures of the ship, including the ship's hull, piers, piling, oil rings, and the internal parts of the pipework used to carry water as a coolant for the shipboard propulsion and power plant, which affects the ship's performance, as it increases the resistance and thereby the engine requires more fuel to overcome these gradual builds on growth-induced resistance), an empirical roughness factor, designed by the Energy EfficientDepartment of the Angelicoussis Group based on internal experimentations, is used. It is estimated as follows:  
\[\textit{RoughnessFactor}=1+\frac{\max(\textit{Days from Delivery, Days from Dry Dock})*2}{365} \tag{1}\]  
where _Days from Delivery_ and _Days from Dry Dock_ are defined as above.  
Finally, regarding the effects of weather on shaft power, the maritime company is using [PERSON]'s method, which employs different models to account for the effects of wind, waves, and currents. By amalgamating wind power, wave power, current power, roughness factor, and multiplying the result by the logarithm of the power model, the performance model was evaluated. This model is used currently in the industry for the same operational and environmental conditions, which will serve as a baseline model for our trained models. While this approach provides an accepted reference, it is inherently limited to short-term, steady-state trials. The accuracy of the method also depends heavily on the availability and quality of trial data and experimentation. Furthermore, [PERSON]'s weather models' prediction accuracy drops dramatically when the weather conditions are above 4 degrees on the Beaufort scale. These limitations underscore the need for more adaptive models, such as those proposed in this study, which leverage broader operational datasets and environmental variability to more accurately represent real-world vessel performance across diverse conditions.