Accurate prediction of the discharge coefficient (Cd) is crucial for the hydraulic design of labyrinth weirs. While conventional vertical-sidewall geometries are widely studied, the synergistic effect of sloped sidewalls and arced planforms remains poorly understood. This study investigates and predicts Cd for arced labyrinth weirs with varying sidewall slopes using a dataset of 277 experimental runs. Five dimensionless parameters ((H0/P), (A/t), (Lc/W), (theta), (phi)), derived via dimensional analysis to capture geometric and hydraulic complexities, were used as inputs for three soft computing approaches: Support Vector Machine (SVM), Gene Expression Programming (GEP), and Artificial Neural Network (ANN). Although all models yielded satisfactory predictions, the Multilayer Perceptron (MLP) ANN model outperformed the others. The optimal MLP 5-9-1 architecture—trained using the BFGS algorithm with a logistic hidden layer and identity output layer activation—achieved training RMSE, MAE, and (R^2) of 0.022, 0.0145, and 0.8402, respectively, and validation metrics of 0.0199, 0.0145, and 0.8961. Graphical analyses confirmed strong agreement between observed and predicted values across all dataset quartiles. These findings demonstrate that the MLP framework offers a robust, reliable alternative for hydraulic design, providing a practical tool for spillway optimization where complex geometric interactions limit traditional linear regressions.