\begin{document} \maketitle \thispagestyle{empty} \begin{abstract} Accurate estimation of a vessel’s speed under varying environmental and operational conditions remains a cornerstone of maritime safety, fuel‑efficiency optimisation, and autonomous navigation. We introduce **MarVelocity**, a novel composite metric that fuses physical‑based hydrodynamic modelling with machine‑learning‑derived correction terms. Using a curated dataset of \num{2.3} million AIS (Automatic Identification System) records combined with high‑resolution oceanographic reanalysis, we train Gradient‑Boosted Regression Trees (GBRT) to predict the \emph{effective speed over ground} (SOG) from a low‑dimensional set of inputs: vessel design parameters, draft, wind, wave, and current vectors. MarVelocity achieves a mean absolute error of \SI{0.12}{\knot} (≈ 3 \% relative) on held‑out test ships, outperforming traditional empirical resistance formulas by a factor of 2.3. We further demonstrate real‑time deployment on a fleet of 150 container ships, reporting a 4.8 \% reduction in fuel consumption over a six‑month trial. The metric is released as an open‑source Python package \texttt{marvelocity} (v1.2) together with reproducible notebooks. \end{abstract}
\subsection{Future Work} \begin{enumerate} \item Extension to **fuel‑consumption** prediction via a joint multi‑task network. \item Incorporation of **ship‑maneuvering** dynamics for autonomous docking. \item Open‑source **benchmark suite** for maritime speed prediction (datasets, evaluation scripts). \end{enumerate} marvelocity pdf
\section{Methodology} \label{sec:method} \subsection{Data Acquisition} \begin{itemize} \item \textbf{AIS}: 2.3 M messages (2018–2023) from the Global Fishing Watch and MarineTraffic APIs. \item \textbf{Oceanographic Reanalysis}: ERA5 \cite{Hersbach2020} providing 10‑m wind vectors, significant wave height, and surface currents at 0.25° resolution. \item \textbf{Ship Catalog}: Technical specifications (length overall, beam, draft, block coefficient, engine power) extracted from the Lloyd’s Register database. \end{itemize} All timestamps are aligned to UTC and interpolated to a 10‑minute cadence. MarVelocity achieves a mean absolute error of \SI{0
\subsection{Baseline Physical Model} We compute the **theoretical speed over ground** $V_{\text{HM}}$ by solving for the equilibrium of propulsive thrust $T$ and total resistance $R_{\text{HM}}$: \begin{equation} R_{\text{HM}}(V) = R_f(V) + R_r(V) + R_a(V) + R_w(V) \,, \end{equation} where $R_f$, $R_r$, $R_a$, and $R_w$ denote frictional, residual, air, and wave resistance respectively (see Holtrop–Mennen \cite{Holtrop1972} for detailed expressions). The thrust is estimated from the ship’s installed power $P$ and propeller efficiency $\eta_p$: \begin{equation} T(V) = \frac{\eta_p P}{V}. \end{equation} The root of $T(V)-R_{\text{HM}}(V)=0$ yields $V_{\text{HM}}$. \end{equation} where $R_f$
\section{Results} \label{sec:results} \subsection{Prediction Accuracy} Table~\ref{tab:accuracy} summarizes error metrics on the held‑out test fleet (150 vessels, 1.1 M observations).
\subsection{Machine‑Learning Approaches} Bai et al. \cite{Bai2021} employed deep neural networks to predict fuel consumption from AIS and weather data, achieving a 5 \% error reduction. Chen and Li \cite{Chen2022} introduced a physics‑informed neural network (PINN) to enforce momentum balance, yet their dataset (≈ 200 k samples) limits generalisation.
\begin{table}[H] \centering \caption{Speed prediction errors (knot) across three methods} \label{tab:accuracy} \begin{tabular}{lccc} \toprule Method & MAE & RMSE & $R^{2}$ \\ \midrule Holtrop–Mennen (baseline) & 0.28 & 0.42 & 0.81 \\ XGBoost residual (ship‑specific) & 0.14 & 0.20 & 0.94 \\ \textbf{MarVelocity (universal)} & \textbf{0.12} & \textbf{0.18} & \textbf{0.96} \\ \bottomrule \end{tabular} \end{table}