Inspired by recent progress in neural-network-assisted solvers and test-function methods for nonlinear evolution equations, we propose a bilinear neural-network framework to derive exact solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. Within this framework, Hirota’s bilinear formulation is coupled with carefully designed neural network ansätze, yielding three novel classes of analytical solutions: breather-rogue waves, previously unreported multi-scale chaotic waves, and periodically interacting travelling waves exhibiting a full \(t=5\) recurrence cycle. These results further enrich the known solution family of the NNV system. To explore the dynamical behaviour behind these patterns, we carry out Duffing-type analysis of the multi-scale chaotic wave solutions. The resulting phase portraits demonstrate a clear transition into a chaotic regime under external driving, marked by high sensitivity to initial conditions and the emergence of characteristic chaotic-attractor geometries. Furthermore, by employing two types of trial functions consistent with the bilinear structure, we also construct general lump solutions as well as general lump-stripe (lump-multi-kink) solutions for the NNV equation. We prove that once a general lump solution for a given (2+1)-dimensional nonlinear evolution equation is available, a corresponding general lump-multi-kink solution with an arbitrary number of kink components can be generated, and the parameter relations from the two trial-function approaches turn out to be consistent. The proposed framework thus provides a useful analytical perspective into the coupling between nonlinear waves and chaotic oscillations, highlighting the promise of neural-network-enhanced bilinear methods for studying complex nonlinear systems.
