@InProceedings{pmlr-v255-monsel24a,
 title =  {Time and State Dependent Neural Delay Differential Equations},
  author =       {Monsel, Thibault and Semeraro, Onofrio and Mathelin, Lionel and Charpiat, Guillaume},
  booktitle =  {Proceedings of the 1st ECAI Workshop on "Machine Learning Meets Differential Equations: From Theory to Applications"},
  pages =  {1--20},
  year =  {2024},
  editor =  {Coelho, Cecilia and Zimmering, Bernd and Costa, M. Fernanda P. and Ferras, Luis L. and Niggemann, Oliver},
  volume =  {255},
  series =  {Proceedings of Machine Learning Research},
  month =  {20 Oct},
  publisher =    {PMLR},
  pdf =  {https://raw.githubusercontent.com/mlresearch/v255/main/assets/monsel24a/monsel24a.pdf},
  url =  {https://proceedings.mlr.press/v255/monsel24a.html},
  abstract =  {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}
}