Evaluating empirical constraints and data augmentation in GA-optimized neural networks for scour prediction around bridge piers

. Accurate prediction of local scour around bridge piers is essential for the safe and economical design of bridge foundations. However, conventional empirical equations are often limited by the experimental conditions under which they were developed, while data-driven models may suffer from data scarcity and limited generalizability. This study develops and evaluates a scour-prediction framework combining data augmentation, Genetic Algorithm-based hyperparameter optimization, and an empirical scour constraint. A literature-derived database containing laboratory and field observations was classified into five pier geometries: cylindrical, round-nosed, square-nosed, sharp-nosed, and grouped piers. Gaussian noise injection was applied separately to each geometry to expand the database to 5,000 samples while preserving the original statistical distributions and inter-variable correlations. Two models were then compared: a Genetic Algorithm-optimized Multilayer Perceptron (GA-MLP) and a Hybrid Deep Learning model incorporating the Froehlich scour equation as a soft constraint in the loss function. Model performance was evaluated using the mean squared error, coefficient of determination, and Kling–Gupta efficiency. Overall, noise augmentation improved predictive generalization, although the degree of improvement depended on pier geometry. The noise-augmented GA-MLP achieved test R2 values ranging from 0.87 to 0.96 and Kling–Gupta efficiencies ranging from 0.84 to 0.97 across the investigated geometries. Its best performance was obtained for grouped piers, with an MSE of 0.0051, R2of 0.96, and KGE of 0.97. For round-nosed piers, it achieved an MSE of 0.0088, R2 of 0.93, and KGE of 0.95. The GA-MLP generally outperformed the empirically constrained model, indicating that imposing a single empirical equation may restrict model flexibility when heterogeneous datasets and pier geometries are considered.