A nonlinear intelligent modeling method is proposed for a class of nonlinear dynamic systems, integrating the recursive least squares method with a forgetting factor and a physical information neural network. This approach facilitates the dynamic modeling of nonlinear systems. The recursive least squares method with a forgetting factor is employed to identify the unknown parameters of a low-order linear model. By incrementally updating the model parameters, the method effectively addresses dynamic changes and parameter jumps within the nonlinear system, gradually refining the model based on data information to enhance accuracy. Following the establishment of the low-order linear model, a physical information neural network is utilized to estimate the unmodeled dynamic unknown increment. Prior knowledge of the mechanism model is incorporated as constraint conditions within the physical information neural network, allowing for rapid convergence to the optimal solution and improved modeling accuracy. This method addresses the challenges posed by insufficient data samples or data corruption in actual industrial processes. The effectiveness of the proposed method is ultimately validated through numerical simulations and comparative experiments.