Burgers_Equation

Burgers' Equation

Intro

This equation describes the movement of a viscous fluid with one spatial (x) and one temporal (t) dimension like a thin ideal pipe with fluid running through it. it describes the speed of fluid at each location along the pipe as time progresses

$$\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} - \nu \frac{\partial^2 u}{\partial x^2} = 0$$

Data Prepration

The boundary condition was taken to be

$$\begin{aligned} u &= 0 \;\;@ x &= 1\\\ u &= 0 \;\;@ x &= -1\\\ u &= -sin(\pi x) \;\;@ t &= 0 \end{aligned}$$

Parameter Study

Adam, 20k	LBFGS, 6.9k, Xavier-Uniform, shuffle	LBFGS, 4.7k, Xavier-Normal, shuffle	LBFGS, 4.7k, Xavier-Uniform, no-shuffle

Acknowledgement

1. data preprocessing was taken from this implementation PINN-Burgers
2. plotting functions were taken from PINN