Neural ODE

Source

Modeling Dynamical Systems With Neural ODE: A Hands-on Guide

What is Neural ODE

In Dynamical Systems, instead of a common ODE

\frac{d u}{d t} = f (u, t) $ $, a n e u r a l O D E e m b e d s a n e u r a l n e t w o r k i n t h e O D E : $ $ \frac{d u}{d t} = f_{N N} (u, t)

What can it help

system identification
- when the explicit form of the ODE is not available, we cannot use traditional ODE
parameter estimation

How does it work

first, recall how traditional ODE works:
- it uses numerical schemes to march the system states in time (with a time-marching equation)
- it uses numerical schemes, e.g. Euler's method
how neural ODE works
- it substitutes the unknown dynamics with neural network and combines with suitable numeral scheme to march the system