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Preprints, Working Papers, ... (Preprint) Year : 2023

Neural State-Dependent Delay Differential Equations

Neural State-Dependent Delay Differential Equations

Abstract

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics, engineering, medicine to economics. These systems are impossible to be properly modelled and simulated with standard Ordinary Differential Equations (ODE), or any data-driven approximation including 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 complicated systems. In this work we revisit the recently proposed Neural DDE by introducing Neural State-Dependent DDE (SDDDE), a general and flexible framework featuring multiple and state-dependent delays. The developed framework is auto-differentiable and runs efficiently on multiple backends. We show that our method is competitive and outperforms other continuous-class models on a wide variety of delayed dynamical systems.
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Dates and versions

hal-04125875 , version 1 (13-06-2023)
hal-04125875 , version 2 (22-06-2023)

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Thibault Monsel, Onofrio Semeraro, Lionel Mathelin, Guillaume Charpiat. Neural State-Dependent Delay Differential Equations. 2023. ⟨hal-04125875v2⟩
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