July 10th, 2020
A brief tutorial on
Neural ODEs
Vikram Voleti
PhD student - Mila, University of Montreal
Visiting Researcher - University of Guelph
Prof. Christopher Pal
Prof. Graham Taylor
voletiv.github.io
@ (virtual) Mila, Montreal, Canada
1. Ordinary Differential Equations (ODEs)
○ Initial Value Problems
○ Numerical Integration methods
○ Fundamental theorem of ODEs
2. Neural ODEs
3. Later research
Vikram Voleti
A brief tutorial on Neural ODEs
2
/ 40
Ordinary Differential Equations (ODEs)
1st order Ordinary Differential Equation:
Vikram Voleti
A brief tutorial on Neural ODEs
3
/ 40
Ordinary Differential Equations (ODEs)
Initial value problem:
Many physical processes follow this template!
Vikram Voleti
A brief tutorial on Neural ODEs
4
/ 40
Ordinary Differential Equations (ODEs)
Initial value problem:
Solution:
Vikram Voleti
A brief tutorial on Neural ODEs
5
/ 40
Ordinary Differential Equations (ODEs)
Initial value problem:
Solution:
What if this cannot be
analytically integrated?
Vikram Voleti
A brief tutorial on Neural ODEs
6
/ 40
Ordinary Differential Equations (ODEs)
Initial value problem:
Solution:
Approximations to
i.e. Numerical Integration :
●
● Runge-Kutta methods
●
Euler method
...
Vikram Voleti
A brief tutorial on Neural ODEs
7
/ 40
Ordinary Differential Equations (ODEs)
Initial value problem:
Solution:
1st-order Runge-Kutta / Euler’s method:
Step size
Update using derivative
Vikram Voleti
A brief tutorial on Neural ODEs
8
/ 40
https://guide.freecodecamp.org/mathematics/differential-equations/eulers-method/