Understanding and accurately predicting the outflow hydrograph from embankment dam breaches is essential for managing the associated flood hazard and improving emergency preparedness. This work simulates the breaching process using a high-resolution 3D computational fluid dynamics (CFD) model, a critical natural hazard for earth-fill dams under overtopping conditions. The model was validated against the experimental data, showing high accuracy in predicting breach development and failure timing. A parametric analysis was performed to assess the influence of the initial breach geometry on erosion dynamics. The results indicated a high sensitivity, while increasing the breach width by 5% led to an average 11% increase in the erosion rate, and decreasing the depth by 5% caused an average 16.5% rise. To enhance predictive capabilities for this hazard, a multilayer neural network (MLNN) was trained on the CFD-generated dataset. The network utilized breach geometry and time as inputs to forecast the peak outflow and erosion rate, achieving excellent accuracy (RMSE = 0.019, R2 = 0.99). This integrated modeling strategy combines data-driven learning with physics-based simulation and demonstrates its effectiveness for laboratory-scale dam breach modeling. This approach is a step toward more efficient surrogate-based tools for flood risk analysis, though its extension to full-scale dams and varied material properties requires additional validation and scaling analyses beyond the scope of this work.