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

Source: arXiv - 2602.18403v1

Overview

This paper tackles a classic problem in maritime engineering: predicting a ship’s main‑engine power from its speed. While off‑the‑shelf machine‑learning models can fit the data, they often ignore the well‑known propeller law (P = cV^{n}) that governs the bulk of the relationship. The authors propose a hybrid “physics‑informed” framework that first applies the analytical power curve and then uses a lightweight ML model to learn only the residual (the part that deviates because of weather, hull fouling, trim, etc.). The result is a model that is both more accurate—especially when data are scarce—and guaranteed to respect the underlying physics.

Key Contributions

• Hybrid modeling pipeline that combines a closed‑form propeller law baseline with a data‑driven residual predictor.
• Comparison of three residual learners – XGBoost, a shallow neural network, and a Physics‑Informed Neural Network (PINN) – against their pure‑data counterparts.
• Demonstration of improved extrapolation in sparsely sampled speed regimes, a known weakness of conventional black‑box regressors.
• Practical validation on real‑world in‑service vessel data, showing consistent gains without added computational overhead.
• Open‑source‑ready recipe for integrating domain knowledge into any regression task where a reliable analytical model exists.

Methodology

1. Baseline physics model

   • The authors start from the calm‑water power curve (P_{\text{base}} = c V^{n}).
   • Coefficients (c) and exponent (n) are obtained from sea‑trial data (or ship design specs) using a simple linear regression on (\log P) vs. (\log V).

2. Residual definition

   • For each observation ((V_i, P_i)) the residual is computed as
     [ r_i = P_i - P_{\text{base}}(V_i) ]
   • This residual captures everything the physics model cannot explain: wind, currents, hull fouling, load distribution, etc.

3. Residual learner

   • Three separate regressors are trained on the residuals:
     • XGBoost – gradient‑boosted trees, robust to heterogeneous features.
     • Shallow Neural Network – a few fully‑connected layers, fast to train.
     • Physics‑Informed Neural Network (PINN) – the same NN but with an extra loss term that penalizes deviation from the baseline physics during training.
   • All models receive the same input feature set (speed, environmental variables, trim, etc.) and output a predicted residual (\hat r).

4. Hybrid prediction

   • Final power estimate is simply
     [ \hat P = P_{\text{base}}(V) + \hat r ]
   • The baseline guarantees that (\hat P) follows the correct asymptotic trend for very low or very high speeds, even when the ML component has never seen such data.

5. Evaluation

   • The dataset is split into dense (well‑covered speeds) and sparse (few observations) regions.
   • Metrics: Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and a physics‑consistency check (e.g., monotonicity of power vs. speed).

Results & Findings

Key take‑aways

• Adding the physics baseline consistently reduces error across all three learners, with the biggest relative improvement (≈30 %) in the sparse speed region.
• The hybrid models preserve the monotonic increase of power with speed, something the pure data‑driven versions occasionally violate.
• Training time remains comparable because the baseline is a closed‑form expression; the residual learners are actually easier to train since they see a smoother target distribution.

Practical Implications

• Weather routing & voyage planning – More reliable power forecasts enable better fuel‑consumption estimates when selecting optimal routes.
• Trim and hull‑form optimization – Engineers can feed the hybrid model into real‑time decision support tools to evaluate how small changes in loading or hull cleanliness affect power demand.
• Regulatory compliance – Accurate power prediction feeds directly into emissions reporting (e.g., IMO EEXI, CII) without needing costly full‑scale sea trials.
• Scalable deployment – The framework requires only a handful of parameters for the baseline and a lightweight ML model, making it suitable for edge devices on board or cloud‑based fleet management platforms.
• Template for other domains – Any system where a solid analytical law exists (aerodynamics, battery discharge, HVAC load) can adopt the same residual‑learning pattern to boost ML performance while staying physically plausible.

Limitations & Future Work

• The baseline curve assumes calm‑water conditions; extreme sea states may introduce non‑linearities that the simple (cV^{n}) form cannot capture.
• The study used a single vessel class; generalizing across ship types (e.g., tankers vs. container ships) may require vessel‑specific baseline calibrations.
• Only three residual learners were examined; exploring Gaussian Processes or deep ensembles could further improve uncertainty quantification.
• Future research could integrate online learning so the residual model continuously adapts to evolving hull conditions (fouling, retrofits) without retraining from scratch.

Bottom line: By letting physics do the heavy lifting and letting machine learning tidy up the leftovers, the authors deliver a model that’s both trustworthy and practical—exactly the kind of hybrid intelligence developers need when real‑world constraints clash with pure data‑driven optimism.

Authors

• Orfeas Bourchas
• George Papalambrou

Paper Information

• arXiv ID: 2602.18403v1
• Categories: cs.LG
• Published: February 20, 2026
• PDF: Download PDF