A machine learning-enhanced Eulerian framework for prediction of near-free-surface underwater explosion bubble dynamics

Predicting bubble dynamics in near-free-surface underwater explosions (NFS-UNDEX) with high fidelity is crucial for engineering design and safety assessment, yet it remains a formidable challenge due to the dominant influence of free-surface effects, which invalidate conventional free-field theories. To bridge this gap, this study develops a novel data-driven framework that synergistically combines Eulerian simulation and a Back Propagation (BP) neural network. The framework is rigorously grounded in experimental validation. A dedicated small-scale underwater explosion test was conducted, providing data that not only verified the fidelity of our three-dimensional Eulerian model but also quantitatively exposed the significant inaccuracy (errors > 10%) of a classic free-field empirical formula (the Geers–Hunter model) under NFS-UNDEX conditions. Leveraging the validated model, a comprehensive dataset of 150 simulations was generated, covering charge masses from 10 to 100 kg and explosion depths from 0.6 to 7.2 m. The dataset encapsulates key parameters: maximum radius (Rmax), pulsation period (PP), time to reach Rmax (Tm), and the height (Hw) and width (Ww) of the accompanying spray dome. A BP neural network trained on this dataset achieves exceptional predictive accuracy. Its errors for Rmax and PP are below 5%, markedly outperforming the empirical formula. The model also reliably predicts spray dome morphology, with median absolute percentage errors below 2% for both height and width, and 95th percentile errors under 5.5%. This work establishes an efficient hybrid framework, validated by experiment, for the high-fidelity prediction of complex NFS-UNDEX bubble dynamics.