A novel approach for discovering stochastic models behind data applied to El Niño–Southern Oscillation

Stochastic differential equations (SDEs) are ubiquitous across disciplines, and uncovering SDEs driving observed time series data is a key scientific challenge. Most previous work on this topic has relied on restrictive assumptions, undermining the generality of these approaches. We present a novel technique to uncover driving probabilistic models that is based on kernel density estimation. The approach relies on few assumptions, does not restrict underlying functional forms, and can be used even on non-Markov systems. When applied to El Niño–Southern Oscillation (ENSO), the fitted empirical model simulations can almost perfectly capture key time series properties of ENSO. This confirms that ENSO could be represented as a two-variable stochastic dynamical system. Our experiments provide insights into ENSO dynamics and suggest that state-dependent noise does not play a major role in ENSO skewness. Our method is general and can be used across disciplines for inverse and forward modeling, to shed light on structure of system dynamics and noise, to evaluate system predictability, and to generate synthetic datasets with realistic properties.