README.md

PDE-Datasets-

This repository contains u,x,t datasets for 4 different Partial Differential Equations(PDEs) at various noise levels

Folders

u,x,t

This folder contains u,x,t values for different equations and different SNRs.

File names

Files are named as i_j.pkl

i values:

1. 1D Diffusion equation: u_t = (0.15) u_{xx}
2. Burgers equation: u_t = (0.1)u_{xx} + (-1)uu_{x}
3. kdv equation: u_t = (-6)uu_{x} + (-1)u_{xxx}
4. 1D Advection equation: u_t = -0.8 u_{x}

j values:

0: Noiseless

1 : SNR = 20000

2 : SNR = 15000

3 : SNR = 10000

4 : SNR = 7500

5 : SNR = 5000

6 : SNR = 3000

7 : SNR = 2000

8 : SNR = 1000

9 : SNR = 800

10 : SNR = 500

11 : SNR = 300

12 : SNR = 200

13 : SNR = 100

14 : SNR = 90

15 : SNR = 80

16 : SNR = 70

17 : SNR = 60

18 : SNR = 50

19 : SNR = 40

20 : SNR = 30

21 : SNR = 20

22 : SNR = 10

23 : SNR = 8

24 : SNR = 6

25 : SNR = 5

26 : SNR = 4

27 : SNR = 3

28 : SNR = 2

29 : SNR = 1

SNR Definition that was used:

u_noisy = u + noise

noise is taken from a normal distribution of mean 0 and variance = var(u)/ SNR

(x,t remains same, noise is added only to u)

Python code for retrieving u,x and t from the .pkl file: (eg: 2_12.pkl)

path_load = "PDE-Datasets/u,x,t"
file_to_read = open(path_load+"/2_12.pkl", "rb")
loaded_dictionary = pickle.load(file_to_read)
u = loaded_dictionary["u"]
x = loaded_dictionary["x"]
t = loaded_dictionary["t"]