Learning the Delay Using Neural Delay Differential Equations

Maria Oprea, Mark Walth, Robert Stephany, Gabriella Torres Nothaft, Arnaldo Rodriguez-Gonzalez +1 more
4/3/2023
math.OCcs.LG

No official code found. Best implementation: punkduckable/NDDE (4 stars, last commit 2024-04-24).

Abstract

The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap between these fields. In this paper, we develop a continuous time neural network approach based on Delay Differential Equations (DDEs). Our model uses the adjoint sensitivity method to learn the model parameters and delay directly from data. Our approach is inspired by that of NODEs and extends earlier neural DDE models, which have assumed that the value of the delay is known a priori. We perform a sensitivity analysis on our proposed approach and demonstrate its ability to learn DDE parameters from benchmark systems. We conclude our discussion with potential future directions and applications.

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Code Implementations(1)

punkduckable/NDDECommunity100%

Neural DDE solver

42Python, Jupyter NotebookMar 28, 20232 years ago

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Cite this paper

@article{oprea2023learning,
  title  = {Learning the Delay Using Neural Delay Differential Equations},
  author = {Maria Oprea and Mark Walth and Robert Stephany and Gabriella Torres Nothaft and Arnaldo Rodriguez-Gonzalez and William Clark},
  year   = {2023},
  eprint = {2304.01329},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2304.01329v2}
}

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