Modeling hydraulic jump roller length on rough beds: a comparative study of ANN and GEP models

Hydraulic jumps (HJs) play a vital role in energy dissipation in hydraulic systems and are critical for the effective design of water management structures. This study employed Artificial Neural Network (ANN) and Gene Expression Programming (GEP) models to predict the roller length ratio ( L * ) of HJs over rough beds. The analysis utilized a dataset of 367 experimental observations with a 70–30 training and testing split. Comprehensive data descriptions were conducted, ensuring a detailed understanding of the inputs, including the upstream Froude number ( F * ), the ratio of initial to sequent HJ depth ( H * = h 2 / h 1 ), and the ratio of channel bed roughness to initial HJ depth ( K * = k s / h 1 ). Descriptive statistics revealed moderate variability and mostly symmetric distributions, making the dataset suitable for predictive modeling. A sensitivity analysis was conducted and confirmed that the depth ratio ( H * ) had the highest influence on L * , followed by F * and K * . The ANN model achieved a training R 2 of 0.937 and a testing R 2 of 0.935, with RMSEs of 1.737 and 1.719, respectively. The GEP model demonstrated a training R 2 of 0.941 and a testing R 2 of 0.930, with RMSEs of 1.682 and 1.780. Both models displayed reliable predictive capabilities, with minimal bias and consistent performance in unseen data, supported by comprehensive error distribution analysis and uncertainty evaluations. Moreover, the models demonstrated a high level of agreement with prior research results, highlighting the importance of thorough data characterization and model validation. Thus, ANN and GEP models have been recognized as effective techniques for predicting hydraulic jump length. Graphical Abstract