Scientific Knowledge-Guided Machine Learning for Vessel Power Prediction: A Comparative Study

TL;DR

A hybrid modeling framework that integrates physics-based knowledge from sea trials with data-driven residual learning is introduced that provides a practical and computationally efficient tool for vessel performance monitoring, with applications in weather routing, trim optimization, and energy efficiency planning.

Abstract

Accurate prediction of main engine power is essential for vessel performance optimization, fuel efficiency, and compliance with emission regulations. Conventional machine learning approaches, such as Support Vector Machines, variants of Artificial Neural Networks (ANNs), and tree-based methods like Random Forests, Extra Tree Regressors, and XGBoost, can capture nonlinearities but often struggle to respect the fundamental propeller law relationship between power and speed, resulting in poor extrapolation outside the training envelope. This study introduces a hybrid modeling framework that integrates physics-based knowledge from sea trials with data-driven residual learning. The baseline component, derived from calm-water power curves of the form $P = cV^n$, captures the dominant power-speed dependence, while another, nonlinear, regressor is then trained to predict the residual power, representing deviations caused by environmental and operational conditions. By constraining the machine learning task to residual corrections, the hybrid model simplifies learning, improves generalization, and ensures consistency with the underlying physics. In this study, an XGBoost, a simple Neural Network, and a Physics-Informed Neural Network (PINN) coupled with the baseline component were compared to identical models without the baseline component. Validation on in-service data demonstrates that the hybrid model consistently outperformed a pure data-driven baseline in sparse data regions while maintaining similar performance in populated ones. The proposed framework provides a practical and computationally efficient tool for vessel performance monitoring, with applications in weather routing, trim optimization, and energy efficiency planning.

Figures (5)

• Figure 1: Calm-water baseline construction. The laden ($P_l$) and ballast ($P_b$) sea-trial curves define the upper and lower bounds, while the combined curve $P_{\mathrm{sea\;trial}}(V,T)$ from Eq. (3) provides the interpolated baseline at intermediate drafts. The red point marks the baseline value at the operating condition $(V,T)$.
• Figure 2: Hybrid model decomposition as expressed in Eq. (4). The laden and ballast sea-trial curves define the calm-water envelope, and the red point indicates the interpolated baseline at $(V,T)$. The black point represents an actual measurement. The vertical bracket labeled $f(\mathbf{X})$ illustrates the learned residual correction added to the baseline to obtain the hybrid prediction.
• Figure 3: Extrapolation behavior of the XGBoost baseline and hybrid models at ballast draft and 5-kn wind. Rows correspond to wind directions of $0^{\circ}$, $90^{\circ}$, and $180^{\circ}$. Red and green curves show the baseline and hybrid predictions, respectively. Blue points denote the nearest training data, while yellow triangles indicate nearest test samples.
• Figure 4: Extrapolation behavior of the NN baseline and hybrid models at ballast draft and 5-kn wind. Rows correspond to wind directions of $0^{\circ}$, $90^{\circ}$, and $180^{\circ}$. Red and green curves show the baseline and hybrid predictions, respectively. Blue points denote the nearest training data, while yellow triangles indicate nearest test samples.
• Figure 5: Extrapolation behavior of the PINN baseline and hybrid models at ballast draft and 5-kn wind. Rows correspond to wind directions of $0^{\circ}$, $90^{\circ}$, and $180^{\circ}$. Red and green curves show the baseline and hybrid predictions, respectively. Blue points denote the nearest training data, while yellow triangles indicate nearest test samples.