Neural State-Dependent Delay Differential Equations

• URL: http://arxiv.org/abs/2306.14545v1
• Date: Mon, 26 Jun 2023 09:35:56 GMT
• Title: Neural State-Dependent Delay Differential Equations
• Authors: Thibault Monsel (DATAFLOT, TAU), Onofrio Semeraro (DATAFLOT), Lionel Mathelin (DATAFLOT), Guillaume Charpiat (TAU)
• Abstract summary: Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics to medicine. 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. We show that our method is competitive and outperforms other continuous-class models on a wide variety of delayed dynamical systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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