Modeling dynamic gas–liquid interfaces in underwater explosions using interval-constrained physics-informed neural networks

Underwater explosion modeling faces a critical challenge of simultaneously resolving shock waves and gas–liquid interfaces, as traditional methods struggle to balance accuracy and computational efficiency. To address this, we develop a physics-informed neural network framework featuring a dual-network architecture, that one network learns flow-field variables (pressure, density, velocity) from simulation data, while another network tracks the gas–liquid interface despite lacking direct numerical solutions. Crucially, we introduce an interval-constraint training strategy that penalizes interface deviations beyond grid spacing limits, paired with a physics-preserving linear mapping of one-dimensional (1D) spherical Euler equations to ensure consistency. Our results show that this approach accurately reconstructs spatiotemporal fields from coarse-grid data, achieving superior computational efficiency over conventional computational fluid dynamics—enabling rapid, mesh-free blast-load analysis for near/far-field scenarios and extensibility to higher-dimensional problems.