Data-driven methods for delay differential equations

Data-driven model discovery is a recent research field at the intersection of Numerical Analysis, Data Science and Dynamical Systems. It focuses on how data can be used to represent and study dynamical systems with special attention to the construction of models that effectively reproduce the system of interest. Dynamical systems generated by ordinary differential equations and partial differential equations have received great interest, while possible applications to delay differential equations remain unexplored. In this talk we will present such possible applications, focusing on how current techniques, like the SINDy algorithm, a procedure used to determine governing equations from data, can be applied to delay differential equations to identify the governing equations, and thus the delay. We will present also how the SINDy algorithm can be used in a multi-fidelity context to reduce the error committed by other data-driven methods, like the dynamic mode decomposition. Numerical results from scalar systems with a single constant delay are presented.

This seminar concerns the results of Alessandro’s MSc thesis (advisor Dimitri Breda, co-advisors Gianluigi Rozza and Nicola Demo from SISSA, Trieste).