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

Abstract. The ENSO system is a complex climate pattern that is crucial in global climate systems and plays a key role in climate prediction. Both statistical methods and numerical models have been dedicated to achieving accurate predictions of ENSO variations; however, there is still a considerable gap in practical applications. Therefore, we proposed a memory kernel function-based approach to solve the inverse problem of ENSO time-varying systems. We attempted to establish differential equations by constructing memory vectors composed of multiple initial values to describe the evolutionary characteristics of this complex system. Unlike traditional inverse problem-solving methods, our research scheme 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 targeted modeling of the ENSO system. 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.