<p>This paper proposes a novel deep learning architecture to solve an inverse source problem for a one-dimensional linear degenerate/singular hyperbolic equation, where both degeneracy and singularity occur at the boundary of the spatial domain. The proposed mesh-free approach approximates the solution and source term using neural networks trained to satisfy the differential operator, initial and boundary conditions, and observability constraints. The method reformulates the inverse problem as an optimization task, minimizing a tailored loss function that incorporates physical constraints and regularization. We demonstrate the effectiveness and robustness of the algorithm through several numerical experiments, showing accurate reconstruction of the source term even in the presence of noise.</p>