This repository contains u,x,t datasets for 4 different Partial Differential Equations(PDEs) at various noise levels
This folder contains u,x,t values for different equations and different SNRs.
Files are named as i_j.pkl
i values:
- 1D Diffusion equation: u_t = (0.15) u_{xx}
- Burgers equation: u_t = (0.1)u_{xx} + (-1)uu_{x}
- kdv equation: u_t = (-6)uu_{x} + (-1)u_{xxx}
- 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
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"]