A self-consistent physics-informed neural network paradigm for sloshing analysis

Abstract

Physics-Informed Neural Networks (PINNs) offer a physically driven alternative to conventional computational fluid dynamics, yet their application to sloshing remains largely unexplored. This paper establishes a self-consistent PINN paradigm for two-dimensional linear sloshing that trains exclusively on physical residuals, requiring no reference data. The dynamic free-surface boundary condition is enforced as a hard constraint, which removes it from the loss function and structurally eliminates the gradient imbalance that dominates conventional penalization-based formulations. This single modification reduces the free-surface elevation error from above 6% to below 2%. Validation against analytical solutions, experimental measurements, and computational fluid dynamic simulations across sway, roll, and combined excitation modes yields median steady-state amplitude deviations below one millimeter across all benchmarks. A systematic ablation study covering six hyperparameter categories and 13 variants isolates the influence of each design choice and yields practical tuning guidance. Because the paradigm relies entirely on physics residuals, it generalizes naturally to configurations for which analytical reference data are unavailable.