This study investigates the Magnetically Impelled Arc Butt welding process for joining low-carbon steel tubes with 27 mm outer diameter and 1.5 mm wall thickness, focusing on the dynamic behavior of the arc and its influence on weld quality. Departing from traditional approaches that emphasize mechanical and metallurgical assessments, this work explores the predictive value of secondary response parameters, specifically arc sound, arc light intensity, and arc temperature. A sensor-integrated data acquisition system was employed to monitor these responses in real time during the welding process. To model and predict these dynamic responses, a Kolmogorov–Arnold Network was developed and optimized using the Exponential Trigonometric Optimization algorithm. Among the models evaluated, the optimized network achieved a coefficient of determination of 0.9889 and a root mean square error of 9.73 decibels for sound intensity prediction, demonstrating high accuracy and strong generalization. These findings highlight the potential of sensor-guided, data-driven modeling as a robust tool for real-time monitoring and control of advanced welding processes.