<p>Time series forecasting plays a crucial role in contemporary production and daily life by analyzing the historical data to predict future trends, patterns, and behaviors across various phenomena. However, forecasting chaotic time series remains a formidable challenge, primarily attributed to the high nonlinearity of chaotic dynamical systems and their extreme sensitivity to noise and initial conditions. In general, predicting through discrete-time models and continuous-time models each have their advantages, but there have been few explorations of their integration. In this paper, we delve into the fusion of these two models by leveraging deep neural networks to achieve a notable improvement in the length and accuracy of chaotic time series prediction. The discrete-time reservoir computing model is utilized to make initial predictions of the chaotic time series, while continuous-time differential equations and Physically Informed Neural Network (PINN) are then adopted to refine the results and mine hidden information from multiple perspectives. The effectiveness of the method is verified by applying it to the Lorenz system. Moreover, we discuss in detail the prediction performance of the method under extreme conditions such as noise, sparse sampling, etc., which reveals satisfactorily results even when a single model fails. By applying the method to an experimental double pendulum system, we further demonstrate the superiority of the method in long-term prediction of real chaotic dynamical systems. Overall, the proposed method represents a new paradigm of multi-method and multi-model fusion, providing innovative ideas for improving the accuracy of chaotic time series prediction.</p>