This study presents a comparative evaluation of three machine learning algorithms— Multivariate Adaptive Regression Splines (MARS), Support Vector Machine (SVM), and Gene Expression Programming (GEP)—for predicting the discharge coefficient (C_d) of labyrinth and piano-key weirs. Experimental data were collected from various linear and arced configurations in a laboratory flume. Dimensional analysis identified four key dimensionless predictors: H_T/P, Fr, L/W, and R/W. The results demonstrated that while all models provided acceptable trends, the optimized MARS architecture exhibited superior statistical performance and stability. In the training phase, MARS achieved an R² of 0.9882, RMSE of 0.0194, and MAE of 0.0157, significantly outperforming SVM (R² = 0.864) and GEP (R² = 0.967). The robustness was further confirmed in the testing phase, where MARS maintained a high R² of 0.9792 and a C_{d(DDR), max} of 6.6331, indicating minimal stochastic variance. Sensitivity analysis revealed that H_T/P and Fr are the most influential parameters, each referenced six times in the MARS validated functions. Furthermore, the Kernel Density Estimation (KDE) and scatter plots validated the high-fidelity alignment of MARS predictions with experimental observations along the 1:1 identity line. The study concludes that the white-box MARS model, with its explicit governing equations and low GCV error (0.000777), serves as the most reliable and transparent computational tool for estimating the hydraulic capacity of complex non-linear weir systems.