import tensorflow.compat.v1 as tf tf.disable_v2_behavior() import numpy as np pi = np.pi sin = np.sin cos = np.cos exp = np.exp sh = np.shape reshape = np.reshape #%% VarNet import from Domain import Domain1D from ADPDE import ADPDE from UtilityFunc import UF uf = UF() sess = tf.Session() from TF_ELM.base_elm import TF_ELM #%% 1D AD-PDE: closed-form solution u = 1.0 # velocity magnitude D = 0.1 / pi # diffusivity T = 2.0 # maximum time bound tlim = [0, T] # time limits # Domain limits: interval = np.array([-1.0, 1.0]) lim = reshape(interval, [2, 1])
import numpy as np
pi = np.pi
sin = np.sin
cos = np.cos
exp = np.exp
shape = np.shape
reshape = np.reshape
from Domain import Domain1D
from ContourPlot import ContourPlot
from ADPDE import ADPDE
from VarNet import VarNet
from UtilityFunc import UF
uf = UF()
import matplotlib.pyplot as plt
from IPython import get_ipython
get_ipython().run_line_magic('matplotlib', 'inline')
#%% PDE input data:
u = 1.0 # velocity magnitude
D = 0.1 / pi # diffusivity
T = 2.0 # maximum simulation time
# Initial condition:
def IC(x):
"""
#%% Modules:
import numpy as np
shape = np.shape
reshape = np.reshape
size = np.size
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras import layers
from tensorflow.python.client import device_lib
from UtilityFunc import UF
uf = UF()
#%% Data Parallelism (Replicated Training)
class TFNN():
"""
Class to construct the tensorflow computational graph and models accross devices.
Attributes:
dim
inpDim
seqLen
depth
layerWidth
modelId
import numpy as np
pi = np.pi
sin = np.sin
cos = np.cos
exp = np.exp
shape = np.shape
reshape = np.reshape
from Domain import Domain1D
from ContourPlot import ContourPlot
from ADPDE import ADPDE
from MOR import MOR
from VarNet import VarNet
from UtilityFunc import UF
uf = UF()
import matplotlib.pyplot as plt
from IPython import get_ipython
get_ipython().run_line_magic('matplotlib', 'inline')
#%% PDE input data:
u = 1.0 # velocity magnitude
T = 2.0 # maximum simulation time
def diffFun(x, t=0, D=0.1/pi):
"""Diffusivity field function."""
return D*np.ones([shape(x)[0], 1])
def IC(x):
functions for a 2D unstructured field which is the solution of the Advection-Diffusion PDE.
Different methods are compared in terms of accuracy and speed. To see the results
simply run the code in a Python console.
For details on the interpolation functions, see the manual at:
https://docs.scipy.org/doc/scipy/reference/interpolate.html
"""
import time
import numpy as np
import scipy.io as spio
from scipy import interpolate
from Domain import PolygonDomain2D
from ContourPlot import ContourPlot
from UtilityFunc import UF
uf = UF()
import matplotlib.pyplot as plt
from IPython import get_ipython
get_ipython().run_line_magic('matplotlib', 'inline')
#%% Data:
mat = spio.loadmat('coord.mat')
coord = mat['coord'] # coordinates
# Exact concentration field:
mat = spio.loadmat('cEx.mat')
cEx = mat['cEx']
cEx = cEx.todense()
shape = np.shape
reshape = np.reshape
sin = np.sin
cos = np.cos
exp = np.exp
pi = np.pi
from scipy import special
erf = special.erf # error function
from Domain import PolygonDomain2D
from ContourPlot import ContourPlot
from ADPDE import ADPDE
from VarNet import VarNet
from UtilityFunc import UF
uf = UF()
import matplotlib.pyplot as plt
# from IPython import get_ipython
# get_ipython().run_line_magic('matplotlib', 'inline')
#%% PDE input data:
#lim = np.array([[0, -0.5], [2, 0.5]]) # spatial domain boundaries
T = 1.5 # maximum simulation time
q = [1., 0.] # velocity magnitude
kappa = 1.e-3 # diffusivity
c0 = 1.0 # concentration value on x=0, |y|<a
a = 0.2 # bounds on the concentration BC
nt = 151 # time discretization number for results