2023/06/26 by Monsel, Thibault, Semeraro, Onofrio, Mathelin, Lionel +1 · 1 citation
#Artificial Intelligence (cs.AI) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.14545
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 \hrefhttps://github.com/thibmonsel/Time-and-State-Dependent-Neural-Delay-Differential-Equationshere.