Electromagnetic launching manufacturing (EMLM) is a high-speed material processing technique powered by pulsed current. The hammer velocity is a key indicator in EMLM, but it is hard to obtain. A viable approach is to use the circuit response current to help in measuring the hammer velocity, but the different curve patterns and the weak interactions between the parameters are major hindrances. In this paper, response current information was used to develop a physics-informed neural network to indirectly predict the hammer velocity. With the experimental dataset, the proposed model had the lowest root mean squared error (0.95) compared with the traditional models (1.62 from Seq2Seq, 1.98 from LSTM, and 2.18 from Attention). This improvement was achieved through the proposed physics-informed neural network architecture. The proposed loss function incorporated knowledge from physics which enabled the model to obtain implicit physical data in the EMLM process, thus enhancing its generalization ability. A fast convergence of the training process was promoted by the developed 2-stage strategy. The introduced attention mechanism added a global perspective that improved the prediction accuracy of the peak velocities. Consequently, our model achieved state-of-the-art predictions of velocities in real-world industrial EMLM systems.