Having garnered significant attention in the scientific community over the past decade, wire-arc directed energy deposition (arc-DED) technology is at the heart of this investigation into additive manufacturing parameters. Singularly focused on Invar as the selected material, the primary objective revolves around devising a virtual sensor for the indirect size measurement of the bead. This innovative methodology involves the seamless integration of internal signals and sensors, enabling the derivation of crucial measurements sans the requirement for direct physical interaction or conventional measurement methodologies. The internal signals recorded, the comprising voltage, the current, the energy from the welding heat source generator, the wire feed speed from the feeding system, the traverse speed from the machine axes, and the temperature from a pyrometer located in the head were all captured through the control of the machine specially dedicated to the arc-DED process during a phase of optimizing and modeling the bead geometry. Finally, a feedforward neural network (FNN), also known as a multi-layer perceptron (MLP), is designed, with the internal signals serving as the input and the height and width of the bead constituting the output. Remarkably cost-effective, this solution circumvents the need for intricate measurements and significantly contributes to the proper layer-by-layer growth process. Furthermore, a neural network model is implemented with a test loss of 0.144 and a test accuracy of 1.0 in order to predict weld bead geometry based on process parameters, thus offering a promising approach for real-time monitoring and defect detection.