Data-driven model discovery has proven to be a powerful approach to recover governing equations of dynamical systems from temporal data series [3]. In particular, the SINDy algorithm, initially proposed for learning the right-hand side of ordinary differential equations [4], has been extended and applied to diverse classes of problems, including stochastic (ordinary) differential equations [1, 7] and rather recently delay differential equations [2, 5, 6]. In this talk we present further developments in view of effectively combining SINDy for stochastic delay differential equations, as well as for equations with distributed terms, including differential equations with distributed delays and renewal equations. Applications range from modeling supply chains to population dynamics. REFERENCES [1]  L. Boninsegna, F. Nuske and C. Clementi, Sparse learning of stochastic dynamical equations, J. Chem. Phys. 148:241723, 2018. [2]  D. Breda, N. Demo, A. Pecile, G. Rozza, Data-driven methods for delay differential equations, IFAC Workshop on Time Delay Systems, 2022. [3]  S.L. Brunton and J.N. Kutz, Data-Driven Science and Engineering – Machine Learning,Dynamical Systems, and Control, Cambridge University Press, 2019. [4]  S.L. Brunton, J.L. Proctor and J.N. Kutz, Discovering governing equations from data by sparse identification of nonlinear dynamical systems, PNAS 113(15):3932-3937, 2016. [5]  A. Sandoz, V. Ducret, G. A. Gottwald, G. Vilmart, and K. Perron, SINDy for delay-differential equations: application to model bacterial zinc response, Proc. Roy. Soc. Lond. A, 479:20220556, 2023. [6]  A. Pecile, N. Demo, M. Tezzele, G. Rozza and D.Breda, Data-driven methods for delay differential equations, J. Comput. Appl. Math., 461:116439, 2025. [7]  M. Wanner and I. Mezic, On higher order drift and diffusion estimates for stochastic SINDy, SIAM J. Appl. Dyn. Sys., 23(2):1504–1539, 2024.