Inverse Differential Equation Modeling of ENSO Prediction Based on Memory Kernel Functions

The El Niño-Southern Oscillation (ENSO) is a complex and influential climate phenomenon critical to understanding global climate systems and enhancing climate predictions. Despite extensive research utilizing both statistical methods and numerical models for accurate ENSO forecasting, significant gaps remain in practical applications. Therefore, we proposed a novel memory kernel function-based approach to solve the inverse problem of ENSO time-varying systems. This method involves constructing differential equations through memory vectors composed of multiple initial values, effectively capturing the system's evolutionary and trends. Unlike traditional inverse problem-solving methods, our research delved into the inherent properties exhibited by ENSO, such as memory and periodicity, and embedded these properties as specific targets in differential equations. By leveraging the flexibility of evolutionary algorithms to solve mathematical problems, we achieved a model targeted at ENSO and predicted at lead times up to 26 months. The results demonstrate that this scheme overcomes the limitations of traditional differential equations with a single initial value and extends these equations to memory vector equations based on multiple initial values. This not only enhances our ability to describe the evolutionary laws of complex systems but also improves the timeliness and reliability of ENSO predictions, achieving encouraging results.