In this study, we endeavor to identify Stochastic Differential Equations (SDEs) characterized by Lévy process noise, focusing on refining the identification method for such SDEs and testing it across varying examples. Our approach integrates data-driven methodologies and deep learning frameworks, enhancing the capability to extract governing laws of dynamical systems effectively, a technique gaining prominence across multiple disciplines.

The current codebase for SDE Identification employs stochastic ResNets to approximate the drift and diffusivity functions within the effective SDE. However, algorithms based on log-likelihood that perform well in Gaussian scenarios struggle and often fail when applied directly to non-Gaussian situations, encountering high error rates and issues with convergence. We overcome some of these challenges by identifying stochastic dynamical systems influenced by α-stable Lévy noise, utilizing solely random pairwise data.