• A hybrid CFD-DNN framework predicts ship motions in irregular waves using residual learning. • The proposed strategy explicitly corrects systematic numerical dissipation and phase lags in RANS simulations. • Swish activation and SmoothL1 loss functions enable high accuracy despite sparse training datasets. • The method reduces computational costs from days to milliseconds to facilitate real-time digital twinning. Accurate time-domain prediction of ship motions in irregular waves is critical for assessing dynamic stability and operability. While Reynolds-Averaged Navier-Stokes (RANS) simulations provide high-fidelity insights, they are constrained by prohibitive computational costs and often exhibit systematic discrepancies, such as numerical dissipation and phase lags, under nonlinear conditions. This paper proposes a data-efficient hybrid modeling framework that synergizes the physical priors of CFD with the nonlinear approximation capability of Deep Neural Networks (DNN) to enhance prediction accuracy. Unlike traditional surrogate models, the proposed architecture employs a residual learning strategy, explicitly training the network to correct the systematic errors between numerical predictions and model test measurements. To address the challenges of data sparsity and experimental noise common in marine engineering, the network incorporates Swish activation functions and a robust SmoothL1 loss function. The framework is validated using experimental data from a Chemical Tanker in irregular waves. Despite being trained on a limited dataset (720 samples), the hybrid model significantly outperforms standalone CFD. Statistical analysis shows a reduction in Mean Absolute Error (MAE) for heave motion from 0.97 m to 0.59 m. The proposed approach reduces computational time from days to milliseconds while maintaining physical consistency, offering a robust tool for digital twinning and rapid design evaluation under data-scarce conditions.
Qi et al. (2026) studied this question.