Surface roughness of deposited or etched film strongly depends on ion bombardment. Relationships between ion bombardment variables and surface roughness are too complicated to model analytically. To overcome this, an empirical neural network model was constructed and applied to a deposition process of silicon nitride (SiN) films. The films were deposited by using a pulsed plasma enhanced chemical vapor deposition system in $SiH_4$-$NH_4$ plasma. Radio frequency source power and duty ratio were varied in the range of 200-800 W and 40-100%. A total of 20 experiments were conducted. A non-invasive ion energy analyzer was used to collect ion energy distribution. The diagnostic variables examined include high (or) low ion energy and high (or low) ion energy flux. Mean surface roughness was measured by using atomic force microscopy. A neural network model relating the diagnostic variables to the surface roughness was constructed and its prediction performance was optimized by using a genetic algorithm. The optimized model yielded an improved performance of about 58% over statistical regression model. The model revealed very interesting features useful for optimization of surface roughness. This includes a reduction in surface roughness either by an increase in ion energy flux at lower ion energy or by an increase in higher ion energy at lower ion energy flux.