Learning the Delay Using Neural Delay Differential Equations
This work addresses a specific bottleneck in modeling dynamical systems with delays for researchers in machine learning and applied mathematics, but it is incremental as it builds on existing neural DDE frameworks.
The paper tackled the problem of learning delay parameters in neural delay differential equations (DDEs) from data, extending prior models that assumed known delays, and demonstrated the approach's ability to learn DDE parameters on benchmark systems.
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.