Sparse identification of nonlinear dynamics for stochastic delay differential equations

• Data-driven system identification of Stochastic Delay Differential Equations. • Compares three practical approaches for estimating drift and diffusion dynamics using four different estimation methods. • A robust method for model discovery in biological and financial systems with memory. A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse identification of nonlinear dynamics. The proposed methodology combines recently proposed high-order estimates of drift and covariance for dealing with stochastic problems with augmented libraries to handle delayed arguments. Three different strategies are discussed in view of exploiting only realistically available data. A thorough comparative numerical investigation is performed on different models, which helps guiding the choice of effective and possibly outperforming schemes.