# Federated Learning for Maritime Environments: Use Cases, Experimental Results, and Open Issues
## 4 FL-Aided Fuel Consumption Prediction
### Performance vs. Spatial Complexity Comparison
Figure 5: Architecture of the four (**A–D**) centralized and decentralized schemes considered for distributed ships’ MEP prediction. For testing the LLMS, LLCI, and FL schemes, the optimal configuration presented in Sections V.C-D was adopted for the local ship models, whereas the CLI scheme showed a minimization of the MEP mean prediction error for \(a=0.001\) and five hidden layers upon extensive training simulations. Figure 6 demonstrates the performance (in terms of accuracy) and the complexity of the deployed schemes. The validation samples included in the accuracy/complexity assessment of all schemes concerned data samples from all ships, all drawn from a dataset that was not encountered during training. To concretely show the relative performance/complexity decrement between schemes, we used normalized measures: all schemes' accuracy (\(1/MAE_{i}\)) was divided by the best-accuracy (\(1/MAE_{min}\)) scheme (i.e., CLI), whereas all schemes' complexity was divided by the lowest-complexity scheme (i.e., LLMS or FL). As clearly evidenced by Figure 6, \(CLI\) presents the highest prediction accuracy, with \(FL\) exhibiting \(11\%\) accuracy reduction relative to \(CLI\). Notably, the LLMS presented the lowest accuracy, attributed to the selfishness of the source model (the model that is transferred to the rest of the models) on its own data. The explanation for the non-effectiveness of this scheme is that it does not have global information about all ships, as opposed to CLI which was trained on the six-ship dataset. It is also observed that the \(LLCI\) shows increased accuracy compared with the \(LLMS\), given that averaging the predictions reduces the error introduced by inferring only one selfish model. Note that, in the LLMS scheme, models are simply transferred and inferred between ships, without any (soft) retraining in the model receiver site. In that case, the LLMS and LLCI schemes' accuracy would be improved at the expense of longer training and time-consuming processes than for FL. For completeness, Table 2 contains quantitative information for comparing CLI and FL in terms of seven evaluation metrics: Normalised Accuracy (\(A_{norm}\)), Goodness of Fit (GoF), Mean Absolute Error (MAE), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE). To have a clear view of the non-normalized MEP accuracy, Figure 7 depicts the actual and predicted MEP curves for the validation samples, including the two best prediction schemes (CLI and FL). Figure 6: Normalized. accuracy (left y-axis, blue) and complexity (right y-axis, black) for the 4 MEP prediction schemes \(CLI\), \(LLMS\), \(LLCI\), and \(FL\). Regarding the complexity, we observed that CLI is 215.2 times more complex than the LLMS and FL schemes, given its high ANN density and size (\(153.6\times 10^{12}\) edges, 3005 units, and 36.9 MB) to achieve the best accuracy. On the contrary, the LLMS and FL schemes show the lowest complexity because they require low-dimensionality ANNs (\(768\times 10^{9}\) edges, 2805 units, and 35.4 MB). Note that the LLCI scheme is six times more complex than the LLMS/FL scheme, since six ANNs are deployed at each ship site (to extract the average prediction), where one ANN per site is required for LLMS and FL.