Neural Network-Based Prediction of Wave Pressure Distribution on Hyperbolic Paraboloid Surfaces

Recent studies have demonstrated the potential of hyperbolic paraboloid (hypar), a doubly curved geometry, in coastal engineering applications. Predicting pressure distribution, critical for subsequent finite element analysis, on such novel three-dimensional structures require Computational Fluid Dynamics (CFD) simulations, which are computationally intensive. To address this challenge, the current study develops an artificial neural network (ANN) surrogate to predict pressure distributions on hypar free-surface breakwaters (FSBWs) under solitary wave loading. Using Smoothed Particle Hydrodynamics (SPH) as the CFD tool, simulations generate the supervised learning dataset, where inputs are the hypar warping R_n, breakwater draft d_r, and wave height H. The targets consist of two 30 × 30 pressure maps at wave arrival (hydrostatic) and peak, together with the wave rise time {P(t₀), P(t_peak), Δt = t_peak − t₀}. Three architectures, FNN, CNN, and DeepONet, are trained with homoscedastic uncertainty loss weighting, each at two parameter sizes (~50k and ~500k). Results for training and testing show that all models achieve low errors, with models with ~50k parameters found to be sufficient, and scaling to ~500k yields some generalization improvement. Further reducing the parameters (~5k) degrades accuracy for all models, with DeepONet proven most robust to parameter size reduction. Overall, this study introduces a novel SPH-ANN workflow for predicting wave pressures on hypar FSBWs, where inference on new samples occurs in a few milliseconds per sample, delivering orders-of-magnitude speedups relative to running new SPH simulations. This computational efficiency enables rapid design iteration and optimization of hypar FSBWs, facilitating their potential deployment in coastal defense.