<p>This paper investigates exact analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili-Boussinesq (KPB) equation using the Bilinear Neural Network Method (BNNM). By combining the Hirota bilinear method with neural network architectures, we construct diverse solution structures including periodic lump solutions, double-lump solutions, superposition of soliton and lump solutions, and breather solutions. The method employs both single-hidden-layer and double-hidden-layer neural network architectures with various activation function combinations to generate rich solution families. Through systematic parameter selection and symbolic computation via Maple, we obtain multiple exact analytical solutions and visualize their dynamical behaviors using three-dimensional plots, density plots, and line plots. Compared to traditional methods, BNNM reduces the number of algebraic equations by approximately 27%-36% when constructing complex interaction solutions, thereby significantly reducing symbolic computation cost. The obtained solutions exhibit significant physical relevance: periodic lump solutions characterize localized propagation in shallow water waves, breather solutions correspond to oscillatory ion-acoustic waves in plasmas, and soliton-lump superposition solutions reflect wave interaction mechanisms in nonlinear optical systems. This research extends the application scope of neural network methods in solving nonlinear partial differential equations and provides valuable insights for understanding wave phenomena in plasma physics, fluid dynamics, and nonlinear optics.</p>