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神经常微分方程教程(来自VIKRAM VOLETI).pdf

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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/
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