Reproduce “Time and State Dependent Neural Delay Differential Equations” on OpenResearch

About this paper

Thibault Monsel, Onofrio Semeraro, Lionel Mathelin, Guillaume Charpiat

Researchers at LISN and INRIA introduced Neural State-Dependent Delay Differential Equations (Neural SDDDEs) and released an accompanying open-source DDE solver capable of modeling non-Markovian dynamical systems with multiple, time- and state-dependent delays. This framework accurately reproduces complex dynamics, achieving superior predictive performance and robustness compared to existing neural ODE variants and Neural Laplace models.

Key insights

• Explicitly modeling time- and state-dependent delays within a neural DDE framework provides higher accuracy in capturing non-Markovian dynamics compared to implicit state space augmentation or Laplace domain transformations.
• Developing a robust DDE solver capable of handling numerical challenges such as discontinuities and situations where delay times are shorter than integration steps is essential for effective neural DDE implementation.
• Neural SDDDE preserves the physical interpretability of the state vector, operating directly within the natural system dimensionality, which is beneficial for scientific understanding and parameter inference, unlike augmented state approaches.

Summary by alphaXiv.