Nonlinear partial differential equations (PDEs) arise naturally in mathematical models of physics, engineering, and finance. Still, their numerical solution remains a challenge due to nonlinearity, high dimensionality, and complex boundary constraints. This paper introduces a novel framework that integrates artificial intelligence (AI), specifically deep neural networks (DNNs), with the mathematical rigour of operator splitting techniques based on the Split System of Common Null Point Equality Problems (SSCNPEP). The proposed AI-SSCNPEP approach synergistically combines neural network approximations with inertial fixed-point iterations to enforce both the PDE structure and essential physical constraints. The framework is demonstrated on two important nonlinear PDEs: The Nonlinear Schrödinger Equation (NLS) and the Fokker–Planck Equation (FP), which appear respectively in quantum mechanics and stochastic modelling. Numerical experiments show improved convergence and robustness over traditional methods, confirming the potential of this hybrid AIoperator paradigm for solving challenging PDEs with theoretical guarantees