Sinusoidal Pulse Width Modulation (SPWM) has traditionally been the preferred control technique for three-phase Voltage Source Inverters (VSIs). However, it tends to generate a significant amount of undesirable interference in the output voltage waveform, leading to increased acoustic noise in connected induction loads. While Random Pulse Width Modulation (RPWM) is often considered a better alternative, it still suffers from inefficient utilization of the DC bus voltage, resulting in residual waveform disturbances. This study explores the use of Artificial Neural Networks (ANNs) to optimize RPWM by more effectively dispersing residual harmonic clusters across a broader frequency spectrum. An ANN-generated signal was integrated into the RPWM control of a three-phase VSI system equipped with a passive LC filter. The performance of this proposed controller was compared with both Dual Random and Fixed Pulse Width Modulation controllers. Power Spectral Density (PSD) and Total Harmonic Distortion (THD) analyses of the output voltages were conducted using MATLAB/Simulink. The results showed that the proposed ANN-based controller achieved consistently lower noise levels and a THD of just 2.17%, without adding complexity or increasing the cost of the modulation strategy.