Speaker
Description
Data-driven model discovery has become a powerful approach for identifying governing equations of dynamical systems using temporal data. The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, initially developed for ordinary differential equations (ODEs) \cite{bpk16}, has been extended to more general classes of problems, recently including also deterministic and stochastic delay differential equations with discrete delays \cite{bbt24,bcd26,pec25}. However, its application to systems with distributed delays and renewal equations remains unexplored.
Distributed delays, at the core of renewal-type integral equations, involve integration over a continuum of past states. Related models are prevalent in biological and ecological applications to describe, e.g., structured populations and epidemics. They portrait memory-dependent dynamics but are challenging to identify due to the inherent complexity of delay kernels and renewal processes. Building on the integral formulation of SINDy for ODEs, we propose a novel extension of the SINDy framework to recover the (possibly nonautonomous) kernel of distributed delays through the use of quadrature formulas. As such the new approach aims at providing a sparse interpretable model rather than just a black-box right-hand side.
We demonstrate the efficacy of the new method first on academic examples and then by applying it to real data of the transmission dynamics of Severe Fever with Thrombocytopenia Syndrome (SFTS) \cite{CSIAM-LS-1-2}, an emerging tick-borne disease.
Bibliography
@article{bbt24,
title={Sparse identification of time delay systems via pseudospectral collocation},
author={Bozzo, E. and Breda, D. and Tanveer, M. },
journal={IFAC-PapersOnLine},
fjournal={IFAC-PapersOnLine},
volume={58},
number={27},
pages={108--113},
year={2024},
publisher={Elsevier}
}
@ARTICLE{bcd26,
Author = {Breda, D and Conte, D and D'Ambrosio, R and Santaniello, T and Tanveer, M},
Journal = {Journal of Computational and Applied Mathematics},
FJournal = {J. Comput. Appl. Math.},
Number = {},
Pages = {117247},
Title = {Sparse identification of Nonlinear Dynamics for Stochastic delay differential equations},
Volume = {479},
Year = {2026}
}
@ARTICLE{bpk16,
Author = {Brunton, S L and Proctor, J L and Kutz, J N},
Journal = {PNAS},
FJournal = {Proceedings of the National Academy of Sciences},
Number = {15},
Pages = {3932-3937},
Title = {Discovering governing equations from data by sparse identification of nonlinear dynamical systems},
Volume = {113},
Year = {2016}
}
@ARTICLE{pec25,
Author = {Pecile, A and Demo, N and Tezzele, M and Rozza, G and Breda, D},
Journal = {J. Comput. Appl. Math.},
FJournal = {Journal of Computational and Applied Mathematics},
Number = {},
Pages = {116439},
Title = {Data-driven methods for delay differential equations},
Volume = {461},
Year = {2025}
}
@Article{CSIAM-LS-1-2,
author = {Zhang, Xue and Haotian, Cui and Zhou, Yi and Jun, Ding and Nah, Kyeongah and Wu, Jianhong},
title = {Patterns of Transmission Dynamics of Severe Fever with Thrombocytopenia Syndrome Virus in Dalian: Roles of Systemic, Co-Feeding, and Transovarial Routes},
journal = {CSIAM Transactions on Life Sciences},
year = {2025},
volume = {1},
number = {2},
pages = {299--319},
issn = {3006-2721},
doi = {https://doi.org/10.4208/csiam-ls.SO-2025-0001},
url = {https://global-sci.com/article/91945/patterns-of-transmission-dynamics-of-severe-fever-with-thrombocytopenia-syndrome-virus-in-dalian-roles-of-systemic-co-feeding-and-transovarial-routes}
}
