Based on the theory of elastic dynamics [1], we propose a generative physical neural network that integrates the partial differential equation (PDE) collocation method. By numerically solving the wave equation, we achieve accurate design of agent materials for dynamic target recognition. First, a generator network is constructed with the wave equation as its physical core. This network combines PDEs with neural networks and introduces a time-recursive structure, treating the material density distribution as a trainable parameter to capture its dynamic response to acoustic wave propagation. Second, the gradient of the loss function with respect to density is computed via backpropagation. The material distribution is iteratively optimized to generate configurations capable of distinguishing the acoustic energy distributions corresponding to different sounds. Finally, a discriminator is incorporated during training to evaluate the match between the acoustic field produced by the generated structure and the target speech. This feedback guides the generator to continuously refine the design variables. As a learning-based numerical approach, the proposed model achieves inverse design for target recognition in nonlinear complex environments. It not only deeply embeds physical mechanisms into the generative model but also offers a new paradigm for material design that integrates data-driven and physics-driven methodologies, effectively overcoming the limitations of traditional approaches in terms of data dependency and interpretability.