Deep Learning-Based Prediction of Ship Roll Motion with Monte Carlo Dropout

Abstract

<jats:p>Accurate prediction of ship roll motion is essential for safe and autonomous navigation. This study presents a deep learning framework that estimates both roll motion and epistemic uncertainty using Monte Carlo (MC) Dropout. Two architectures, a Long Short-Term Memory (LSTM) network and a Transformer encoder, were trained on HydroD？Wasim simulations covering various sea states, speeds, and damage conditions, and validated with real voyage data from two ferries, showing complementary performance, where LSTM achieved higher accuracy and Transformer provided more reliable confidence intervals. Model performance was evaluated by mean squared error (MSE), prediction interval coverage probability (PICP), and prediction interval normalized average width (PINAW). The LSTM achieved lower MSE, showing superior deterministic accuracy, while the Transformer produced higher PICP and wider PINAW, indicating more reliable uncertainty estimation. Results confirm that MC Dropout effectively quantifies epistemic uncertainty, improving the reliability of deep learning？based ship motion forecasting for intelligent maritime operations.</jats:p>