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A general framework for neural delay differential equations with various delay types.

Jiaxuan Zhang^1,2, Qunxi Zhu^2,3,4, Wei Lin^1,2,3,4,5

¹School of Mathematical Sciences, Fudan University, Shanghai 200433, China.

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Summary

This summary is machine-generated.

This study introduces Generalized Neural Delay Differential Equations (GNDDEs) for modeling complex systems with various delays. A novel simulation-free training method enables efficient system reconstruction from irregular time series data.

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Area of Science:

Machine Learning
Dynamical Systems
Neural Networks

Background:

Neural Delay Differential Equations (NDDEs) offer a continuous-depth neural network framework.
Previous NDDEs primarily handled constant delays.

Purpose of the Study:

To generalize NDDEs to handle diverse delay types (time-dependent, state-dependent).
To develop a simulation-free training strategy for vector field reconstruction.
To enable adaptive, model-free identification of delay functions and model-based parameter identification.

Main Methods:

Introduction of Generalized NDDEs (GNDDEs) to accommodate various delay functions.
Implementation of a simulation-free training approach using regression between preprocessed target and parameterized vector fields.
Bypassing numerical differential equation solving for time-series regression.

Main Results:

Demonstrated effectiveness and computational efficiency of GNDDEs across various delay differential equation problems.
Successful system reconstruction from irregularly sampled time series without prior model knowledge.
Adaptive identification of delay functions and model parameters achieved.

Conclusions:

GNDDEs provide a versatile framework for modeling complex delay systems.
The simulation-free training strategy enhances applicability and efficiency.
This work expands the utility of continuous-depth neural networks in delay system modeling.