2024-10-06-monsel24a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Time and State Dependent Neural Delay Differential Equations	Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard Ordinary Differential Equations (ODE), or data-driven approximations such as Neural Ordinary Differential Equations (NODE). To circumvent this issue, latent variables are typically introduced to solve the dynamics of the system in a higher dimensional space and obtain the solution as a projection to the original space. However, this solution lacks physical interpretability. In contrast, Delay Differential Equations (DDEs), and their data-driven approximated counterparts, naturally appear as good candidates to characterize such systems. In this work we revisit the recently proposed Neural DDE by introducing Neural State-Dependent DDE (SDDDE), a general and flexible framework that can model multiple and state- and time-dependent delays. We show that our method is competitive and outperforms other continuous-class models on a wide variety of delayed dynamical systems. Code is available at the repository https://github.com/thibmonsel/Time-and-State-Dependent-Neural-Delay-Differential-Equations	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	monsel24a	0	Time and State Dependent Neural Delay Differential Equations	1	20	1-20	1	false	Monsel, Thibault and Semeraro, Onofrio and Mathelin, Lionel and Charpiat, Guillaume	given family Thibault Monsel given family Onofrio Semeraro given family Lionel Mathelin given family Guillaume Charpiat	2024-10-06		Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications"	255	inproceedings	date-parts 2024 10 6	https://raw.githubusercontent.com/mlresearch/v255/main/assets/monsel24a/monsel24a.pdf