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

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.