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This article presents a new prediction model, the ordinary differential equations–memory kernel function (ODE–MKF), constructed from multiple backtracking initial values (MBIV). The model is similar to a simplified numerical model after spatial dimension reduction and has both nonlinear characteristics and the low-cost advantage of a time series model. The ODE–MKF focuses on utilizing more temporal information and includes machine learning to solve complex mathematical inverse problems to establish a predictive model. This study first validates the feasibility of the ODE–MKF via experiments using the Lorenz system. The results demonstrate that the ODE–MKF prediction model could describe the nonlinear characteristics of complex systems and exhibited ideal predictive robustness. The prediction of the El Niño-Southern Oscillation (ENSO) index further demonstrates its effectiveness, as it achieved 24-month lead predictions and effectively improved nonlinear problems. Furthermore, the reliability of the model was also tested, and approximately 18 months of prediction were achieved, which was verified with the Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) radiation fluxes. The short-term memory index Southern Oscillation (SO) was further used to examine the applicability of ODE–MKF. A six-month lead prediction of the SO trend was achieved, indicating that the predictability of complex systems is related to their inherent memory scales.