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Sparse regression techniques enable the extraction of governing equations directly from measurement data, allowing efficient identification of nonlinear system dynamics with minimal complexity. This work presents algorithmic aspects of the data-driven method SINDy (Sparse Identification of Nonlinear Dynamics) [3] for the identification of the dynamics of Itô SDEs and SDDEs with a single discrete delay. We use single-path reconstructions to obtain time-series data of the stochastic process and different Itô-Taylor based estimators to obtain the intrisic drift and diffusion functions [4]. We present a comparative computational analysis on some SDEs and SDDEs models testing this single-path approach in combination with all the estimation strategies [1][2]. This work falls within the activities of PRIN-MUR 2022 project “Stochastic numerical modelling for sustainable innovation”, CUP: E53D23017940001, granted by the Italian Ministry of University and Research within the framework of the Call relating to the scrolling of the final rankings of the PRIN 2022 call.
[1] Breda, D., Conte, D., D’Ambrosio, R., Santaniello, I., Tanveer, M. (2026) Sparse Identification of Nonlinear Dynamics for Stochastic Delay Differential Equations. J. Comput. Appl. Math., Vol. 479, pp. 117247.
[2] Breda, D., Conte, D., D’Ambrosio, R., Santaniello, I., Tanveer, M. (Submitted) A Matlab code for discovering governing dynamics in Stochastic Differential Equations using SINDy algorithm and Itô-Taylor based approximation.
[3] Brunton, S.L., Proctor, J.L., Kutz, J.N. (2016) Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS, Vol. 113, pp. 3932-3937.
[4] Wanner, M., Mezic, I. (2024) On Higher Order Drift and Diffusion Estimates for Stochastic SINDy. arXiv:2306.17814.