Physics-Informed Machine Learning for Vessel Shaft Power and Fuel Consumption Prediction: Interpretable KAN-based Approach

TL;DR

Using operational and environmental data from five cargo vessels, PI-KAN consistently outperforms the traditional polynomial method and neural network baselines, and achieves the lowest mean absolute error and root mean squared error, and the highest coefficient of determination, for shaft power and fuel consumption across all vessels.

Abstract

Accurate prediction of shaft rotational speed, shaft power, and fuel consumption is crucial for enhancing operational efficiency and sustainability in maritime transportation. Conventional physics-based models provide interpretability but struggle with real-world variability, while purely data-driven approaches achieve accuracy at the expense of physical plausibility. This paper introduces a Physics-Informed Kolmogorov-Arnold Network (PI-KAN), a hybrid method that integrates interpretable univariate feature transformations with a physics-informed loss function and a leakage-free chained prediction pipeline. Using operational and environmental data from five cargo vessels, PI-KAN consistently outperforms the traditional polynomial method and neural network baselines. The model achieves the lowest mean absolute error (MAE) and root mean squared error (RMSE), and the highest coefficient of determination (R^2) for shaft power and fuel consumption across all vessels, while maintaining physically consistent behavior. Interpretability analysis reveals rediscovery of domain-consistent dependencies, such as cubic-like speed-power relationships and cosine-like wave and wind effects. These results demonstrate that PI-KAN achieves both predictive accuracy and interpretability, offering a robust tool for vessel performance monitoring and decision support in operational settings.

Figures (5)

• Figure 1: Architecture of the Physics-Informed Kolmogorov–Arnold Network (PI-KAN) for vessel performance modeling. The model applies per-feature univariate transformations followed by a linear combination layer, incorporates a physics-informed loss for propulsion consistency, and uses a leakage-free chained pipeline (RPM $\rightarrow$ shaft power $\rightarrow$ fuel consumption) with out-of-fold stacking to ensure physically plausible and robust multi-stage predictions as described in the Figure \ref{['fig:architecture-chained-prediction-vessel-performnace']}.
• Figure 2: Leakage-free chained prediction pipeline used in PI-KAN: shaft RPM is predicted first, followed by shaft power and then fuel consumption, with each stage receiving out-of-fold (OOF) predictions from the previous one to avoid target leakage and preserve physical causality.
• Figure 3: Comparison of actual vs predicted performance metrics for A-6 Vessel.
• Figure 4: Adversarial weather response (A–1 vs. A–11): vessel speed as a function of wave height. A–11 reduces speed at higher waves, while A–1 holds a near-constant setpoint. This difference aligns with Table \ref{['tab:voyage-summary']}: lower error on A–11 (ME=+5.55%, MAPE=10.17%) versus higher error on A–1 (ME=+22.41%, MAPE=22.63%).
• Figure 5: Learned univariate feature transformation functions of the KAN model for shaft power prediction (epoch 76). Each subplot shows how an input feature is nonlinearly mapped before combination in the network. The transformations reflect physically meaningful patterns, including cubic-like dependence on ship speed through water (stw_ms), cosine-like wind and wave directional effects, and localized nonlinear responses to swell and sea depth. The top-left subplot displays the training loss curve converging after $\sim$60 epochs.