A Hybrid Machine Learning Model For Ship Speed Through Water: Solve And Predict

The maritime transport industry faces a significant challenge: reducing its greenhouse gas (GHG) emissions by 50% compared to 2008 levels. A crucial factor in calculating and optimizing these emissions is accurately predicting ship speed through water. While various models exist, few effectively combine both physical principles and machine learning approaches, leading to limitations in prediction accuracy.

The paper proposes a hybrid model with two main components: ''Solve'' Component: A physics-based approach that uses a Physics-Informed Neural Network (PINN) to determine the theoretical speed a ship would achieve in calm water conditions, based on fundamental physical principles and equations. ''Predict'' Component: A data-driven approach that takes the theoretical calm water speed and adjusts it based on real-world conditions using machine learning algorithms, producing actual speed predictions.

The Solve Phase centers around a differential equation relating three key parameters: propulsion power (P), draft (T), and speed through calm water (V_w), the equation takes the form:

The model uses a PINN to solve a differential equation that links propulsion power (P), draft (T), and calm water speed (V_w) to generate initial speed estimates. The PINN uses a loss function that incorporates both initial conditions and differential equation residuals. A major challenge arises because V_w is theoretical and cannot be directly measured. This issue is addressed using historical data by identifying periods when sea conditions were calm to use as training data.

The model creates a bridge between its solve and predict phases. In the first approach, focused on training data generation, the system utilizes the trained PINN to generate collocation points. From these points, it creates training triplets consisting of propulsion power (P_i), draft (T_i), and calm water speed (V_wi). This approach uses a straightforward mean squared error loss function to train the neural network. The second approach takes a different path by using propulsion power (P) and draft (T) as direct inputs to the neural network. What makes this approach unique is that it incorporates the PINN directly into the loss function. This integration allows physical principles from the differential equation to directly influence the predictions, creating a stronger connection between the physical model and the machine learning component.

The predict phase begins by taking the calm water speed predictions generated from the solve phase and enhances them by incorporating various real-world factors that affect ship movement. These factors include maritime conditions, meteorological data, and current conditions, providing a comprehensive view of the actual sailing environment. To process this combined data, we use machine learning algorithms such as Xgboost. The final output of this phase is the real speed through water (V_wr), which represents a more realistic prediction that accounts for all environmental factors affecting the ship's speed.

The model offers a groundbreaking approach to maritime speed prediction by generalizing across vessel types and integrating physical principles with machine learning. By incorporating operational and meteorological data, it provides more accurate speed predictions that optimize fuel consumption and support the maritime industry's greenhouse gas emission reduction goals, bridging environmental protection with operational efficiency.