# Learning the Delay Using Neural Delay Differential Equations

arXiv: https://arxiv.org/abs/2304.01329 · HTML: https://mlsanity.com/paper/2304.01329/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Delay Differential Neural Networks](https://mlsanity.com/paper/2012.06800/) (2020)
- [Neural Piecewise-Constant Delay Differential Equations](https://mlsanity.com/paper/2201.00960/) (2022)

## Built on by (most cited first, 2 of 2)

- [Weak-PDE-LEARN: A Weak Form Based Approach to Discovering PDEs From Noisy, Limited Data](https://mlsanity.com/paper/2309.04699/) (2023)
- [Neural delay differential equations: learning non-Markovian closures for partially known dynamical systems](https://mlsanity.com/paper/2410.02843/) (2024)

## Abstract (arXiv)

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.