Sparse Identification of Nonlinear Dynamics for Stochastic Delay Differential Equations

TL;DR

This paper introduces a novel framework combining SINDy with delay and stochastic analysis techniques to identify nonlinear stochastic delay differential equations from data.

Contribution

It extends the SINDy algorithm to stochastic delay differential equations, incorporating delay handling and stochastic estimation methods for the first time.

Findings

Effective identification of stochastic delay dynamics demonstrated.

Comparison of strategies guides practical application.

Framework outperforms existing methods in numerical tests.

Abstract

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.