<p>This paper employs the Deep–Galerkin–Method (DGM) to approximate solutions to the hyperbolic telegraphic equation (hTE), a significant hyperbolic partial differential equation (hPDE) that models various phenomena in applied sciences. hPDEs are fundamental in describing structural vibrations and form the basis for atomic physics equations. The DGM utilizes a deep neural network (DNN) that satisfies initial conditions (ICs), boundary conditions (BCs), and the differential operator (DO). Training occurs on randomly selected batches of time and space points, eliminating the need for mesh formation. The Adam optimizer is used to optimize the DNN parameters. To enhance DGM efficiency, we propose a novel DNN architecture resembling a multiplicative long short-term memory (mLSTM) network. Additionally, we implement neuron-wise locally adaptive activation functions instead of traditional activation functions. Our experimental results demonstrate significant improvements compared to recent methods, including the B-spline method, the Polynomial scaling functions method, and the Interpolating scaling functions method.</p>