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ojits01_synthetic.py
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ojits01_synthetic.py
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"""
@author: Archie Huang
Built upon Dr. Maziar Raissi's PINNs - https://github.com/maziarraissi/PINNs
Use Tensorflow 1.x
"""
import random
import tensorflow as tf
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import scipy.io
from scipy.interpolate import griddata
from pyDOE import lhs
import time
import matplotlib.gridspec as gridspec
from mpl_toolkits.axes_grid1 import make_axes_locatable
from matplotlib.ticker import MultipleLocator
import os
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '3'
se = 1
np.random.seed(se)
tf.set_random_seed(se)
# PINN Class
class PhysicsInformedNN:
def __init__(self, X_u, u, X_f, layers, lb, ub):
self.lb = lb
self.ub = ub
self.x_u = X_u[:,0:1]
self.t_u = X_u[:,1:2]
self.x_f = X_f[:,0:1]
self.t_f = X_f[:,1:2]
self.u = u
self.layers = layers
self.weights, self.biases = self.initialize_NN(layers)
self.sess = tf.Session(config=tf.ConfigProto(allow_soft_placement=True,
log_device_placement=True))
self.x_u_tf = tf.placeholder(tf.float32, shape=[None, self.x_u.shape[1]])
self.t_u_tf = tf.placeholder(tf.float32, shape=[None, self.t_u.shape[1]])
self.u_tf = tf.placeholder(tf.float32, shape=[None, self.u.shape[1]])
self.x_f_tf = tf.placeholder(tf.float32, shape=[None, self.x_f.shape[1]])
self.t_f_tf = tf.placeholder(tf.float32, shape=[None, self.t_f.shape[1]])
self.u_pred = self.net_u(self.x_u_tf, self.t_u_tf)
self.f_pred = self.net_f(self.x_f_tf, self.t_f_tf)
self.loss = tf.reduce_mean(tf.square(self.u_tf - self.u_pred)) + tf.reduce_mean(tf.square(self.f_pred))
self.optimizer = tf.contrib.opt.ScipyOptimizerInterface(self.loss,
method = 'L-BFGS-B',
options = {'maxiter': 10000,
'maxfun': 10000,
'maxcor': 50,
'maxls': 20,
'ftol' : 2.220446049250313e-09})
init = tf.global_variables_initializer()
self.sess.run(init)
def initialize_NN(self, layers):
weights = []
biases = []
num_layers = len(layers)
for l in range(0, num_layers-1):
W = self.xavier_init(size=[layers[l], layers[l+1]])
b = tf.Variable(tf.zeros([1,layers[l+1]], dtype=tf.float32), dtype=tf.float32)
weights.append(W)
biases.append(b)
return weights, biases
def xavier_init(self, size):
in_dim = size[0]
out_dim = size[1]
xavier_stddev = np.sqrt(2/(in_dim + out_dim))
return tf.Variable(tf.truncated_normal([in_dim, out_dim], stddev=xavier_stddev), dtype=tf.float32)
def neural_net(self, X, weights, biases):
num_layers = len(weights) + 1
H = 2.0*(X - self.lb)/(self.ub - self.lb) - 1.0
for l in range(0,num_layers-2):
W = weights[l]
b = biases[l]
H = tf.tanh(tf.add(tf.matmul(H, W), b))
W = weights[-1]
b = biases[-1]
Y = tf.add(tf.matmul(H, W), b)
return Y
def net_u(self, x, t):
u = self.neural_net(tf.concat([x,t],1), self.weights, self.biases)
return u
def net_f(self, x,t):
u = self.net_u(x,t)
u_t = tf.gradients(u, t)[0]
u_x = tf.gradients(u, x)[0]
f = 0.15 * u_x - 0.012 * u * u_x - 0.006 * u_t
return f
def callback(self, loss):
print('Loss:', loss)
def train(self):
tf_dict = {self.x_u_tf: self.x_u, self.t_u_tf: self.t_u, self.u_tf: self.u,
self.x_f_tf: self.x_f, self.t_f_tf: self.t_f}
self.optimizer.minimize(self.sess,
feed_dict = tf_dict,
fetches = [self.loss],
loss_callback = self.callback)
def predict(self, X_star):
u_star = self.sess.run(self.u_pred, {self.x_u_tf: X_star[:,0:1], self.t_u_tf: X_star[:,1:2]})
f_star = self.sess.run(self.f_pred, {self.x_f_tf: X_star[:,0:1], self.t_f_tf: X_star[:,1:2]})
return u_star, f_star
# Regular NN class
class NN:
def __init__(self, X_u, u, X_f, layers, lb, ub):
self.lb = lb
self.ub = ub
self.x_u = X_u[:,0:1]
self.t_u = X_u[:,1:2]
self.x_f = X_f[:,0:1]
self.t_f = X_f[:,1:2]
self.u = u
self.layers = layers
self.weights, self.biases = self.initialize_NN(layers)
self.sess = tf.Session(config=tf.ConfigProto(allow_soft_placement=True,
log_device_placement=True))
self.x_u_tf = tf.placeholder(tf.float32, shape=[None, self.x_u.shape[1]])
self.t_u_tf = tf.placeholder(tf.float32, shape=[None, self.t_u.shape[1]])
self.u_tf = tf.placeholder(tf.float32, shape=[None, self.u.shape[1]])
self.x_f_tf = tf.placeholder(tf.float32, shape=[None, self.x_f.shape[1]])
self.t_f_tf = tf.placeholder(tf.float32, shape=[None, self.t_f.shape[1]])
self.u_pred = self.net_u(self.x_u_tf, self.t_u_tf)
self.f_pred = self.net_f(self.x_f_tf, self.t_f_tf)
self.loss = tf.reduce_mean(tf.square(self.u_tf - self.u_pred))
self.optimizer = tf.contrib.opt.ScipyOptimizerInterface(self.loss,
method = 'L-BFGS-B',
options = {'maxiter': 10000,
'maxfun': 10000,
'maxcor': 50,
'maxls': 20,
'ftol' : 2.220446049250313e-09})
init = tf.global_variables_initializer()
self.sess.run(init)
def initialize_NN(self, layers):
weights = []
biases = []
num_layers = len(layers)
for l in range(0, num_layers-1):
W = self.xavier_init(size=[layers[l], layers[l+1]])
b = tf.Variable(tf.zeros([1,layers[l+1]], dtype=tf.float32), dtype=tf.float32)
weights.append(W)
biases.append(b)
return weights, biases
def xavier_init(self, size):
in_dim = size[0]
out_dim = size[1]
xavier_stddev = np.sqrt(2/(in_dim + out_dim))
return tf.Variable(tf.truncated_normal([in_dim, out_dim], stddev=xavier_stddev, seed=se), dtype=tf.float32)
def neural_net(self, X, weights, biases):
num_layers = len(weights) + 1
H = 2.0*(X - self.lb)/(self.ub - self.lb) - 1.0
for l in range(0,num_layers-2):
W = weights[l]
b = biases[l]
H = tf.tanh(tf.add(tf.matmul(H, W), b))
W = weights[-1]
b = biases[-1]
Y = tf.add(tf.matmul(H, W), b)
return Y
def net_u(self, x, t):
u = self.neural_net(tf.concat([x,t],1), self.weights, self.biases)
return u
def net_f(self, x,t):
u = self.net_u(x,t)
u_t = tf.gradients(u, t)[0]
u_x = tf.gradients(u, x)[0]
f = 0.15 * u_x - 0.012 * u * u_x - 0.006 * u_t
return f
def callback(self, loss):
print('Loss:', loss)
def train(self):
tf_dict = {self.x_u_tf: self.x_u, self.t_u_tf: self.t_u, self.u_tf: self.u,
self.x_f_tf: self.x_f, self.t_f_tf: self.t_f}
self.optimizer.minimize(self.sess,
feed_dict = tf_dict,
fetches = [self.loss],
loss_callback = self.callback)
def predict(self, X_star):
u_star = self.sess.run(self.u_pred, {self.x_u_tf: X_star[:,0:1], self.t_u_tf: X_star[:,1:2]})
f_star = self.sess.run(self.f_pred, {self.x_f_tf: X_star[:,0:1], self.t_f_tf: X_star[:,1:2]})
return u_star, f_star
if __name__ == "__main__":
N_u = 1000
N_f = 10000
layers = [2, 20, 20, 20, 20, 20, 20, 20, 20, 1]
data = scipy.io.loadmat('data/synthetic.mat')
t = data['tScale'].T.flatten()[:,None]
x = data['xScale'].T.flatten()[:,None]
Exact = np.real(data['v'])
X, T = np.meshgrid(x,t)
X_star = np.hstack((X.flatten()[:,None], T.flatten()[:,None]))
u_star = Exact.flatten()[:,None]
lb = X_star.min(0)
ub = X_star.max(0)
################################# CAV Plot ####################################
N_cav = 30
cav = np.real(data['N'])
idx_cav = np.sort(random.sample(range(int(cav.min()), int(cav.max())), N_cav))
contr = plt.contour(X, T, cav, idx_cav)
plt.title('CAV Trajectories', fontsize = 16)
plt.ylabel('Time $t$ (s)', fontsize = 14)
plt.xlabel('Location $x$ (m)', fontsize=14)
plt.savefig('figures/cav{}_trajectory.pdf'.format(N_cav))
plt.savefig('figures/cav{}_trajectory.eps'.format(N_cav))
# plt.show()
################################# CAV Plot ####################################
################################# CAV Samples #################################
X_u_train = contr.collections[0].get_paths()[0].vertices
for a in range(1, N_cav):
path = contr.collections[a].get_paths()[0]
ver = path.vertices
X_u_train = np.vstack([X_u_train, ver])
print("Total Trajectory Data Points: ", len(X_u_train), '\n')
################################# CAV Samples #################################
################################# Filters #####################################
# RSU communication range and locations
comm_range = 300
loca = [0, 1000, 2000, 3000, 4000, 5000]
mask = ((X_u_train[:, 0] < loca[0] + comm_range) |
((loca[1] - comm_range < X_u_train[:, 0]) & (X_u_train[:, 0] < loca[1] + comm_range)) |
((loca[2] - comm_range < X_u_train[:, 0]) & (X_u_train[:, 0] < loca[2] + comm_range)) |
((loca[3] - comm_range < X_u_train[:, 0]) & (X_u_train[:, 0] < loca[3] + comm_range)) |
((loca[4] - comm_range < X_u_train[:, 0]) & (X_u_train[:, 0] < loca[4] + comm_range)) |
(loca[5] - comm_range < X_u_train[:, 0]))
X_u_train = X_u_train[mask]
X_u_train = np.rint(X_u_train)
X_u_train[:, 0] = np.rint(X_u_train[:, 0] / 5) * 5 # fit for 5-meter bins
X_u_train = np.unique(X_u_train, axis=0).astype(int)
print("Total RSU Data Points: ", len(X_u_train), '\n')
################################# Filters #####################################
############################### Training Data #################################
idx = np.random.choice(X_u_train.shape[0], N_u, replace=False)
X_u_train = X_u_train[idx, :]
X_f_train = lb + (ub-lb)*lhs(2, N_f)
X_f_train = np.vstack((X_f_train, X_u_train))
u_train = np.empty([N_u, 1])
for i in range(0, N_u):
u_train[i] = Exact[X_u_train[i][1]][int(X_u_train[i][0] / 5)]
############################### Training Data #################################
# PINN Model
model = PhysicsInformedNN(X_u_train, u_train, X_f_train, layers, lb, ub)
start_time = time.time()
model.train()
elapsed = time.time() - start_time
print('Training time: %.4f' % elapsed)
u_pred, f_pred = model.predict(X_star)
error_u = np.linalg.norm(u_star-u_pred,2)/np.linalg.norm(u_star,2)
print('Error u: %e' % error_u)
U_pred = griddata(X_star, u_pred.flatten(), (X, T), method='cubic')
Error = np.abs(Exact - U_pred)
# Regular NN Model
model2 = NN(X_u_train, u_train, X_f_train, layers, lb, ub)
start_time2 = time.time()
model2.train()
elapsed2 = time.time() - start_time2
print('Training time: %.4f' % elapsed2)
u_pred2, f_pred2 = model2.predict(X_star)
error_u2 = np.linalg.norm(u_star-u_pred2,2)/np.linalg.norm(u_star,2)
print('Error u: %e' % error_u2)
U_pred2 = griddata(X_star, u_pred2.flatten(), (X, T), method='cubic')
Error2 = np.abs(Exact - U_pred2)
################################# Plot #################################
pgf_with_latex = { # setup matplotlib to use latex for output
"pgf.texsystem": "pdflatex",
"text.usetex": True,
"font.family": "serif",
"pgf.preamble": [
r"\usepackage[utf8x]{inputenc}",
r"\usepackage[T1]{fontenc}",
]
}
mpl.rcParams.update(pgf_with_latex)
fig = plt.figure(figsize=(8, 6.5))
####### Row 0: PIDL: u(t,x) ##################
gs0 = gridspec.GridSpec(1, 2)
gs0.update(top=0.9, bottom=0.6, left=0.15, right=0.85, wspace=0)
ax = plt.subplot(gs0[:, :])
ax.tick_params(axis='both', which='major', labelsize=20)
ax.yaxis.set_major_locator(MultipleLocator(60))
h = ax.imshow(U_pred, interpolation='nearest', cmap='RdBu',
extent=[x.min(), x.max(), t.min(), t.max()],
origin='lower', aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
cax.tick_params(labelsize=20)
fig.colorbar(h, cax=cax, ticks=[5, 10, 15, 20])
ax.plot(X_u_train[:, 0], X_u_train[:, 1], 'kx', markersize=0.8, clip_on=False)
ax.set_ylabel('Time $t$ (s)', fontsize=20)
ax.set_xlabel('Location $x$ (m)', fontsize=20)
ax.legend(frameon=False, loc='best', fontsize=20)
ax.set_title('PIDL Estimation $v (x,t)$ (m/s)', fontsize=20)
####### Row 1: DL: u(t,x) ##################
gs1 = gridspec.GridSpec(1, 2)
gs1.update(top=0.4, bottom=0.1, left=0.15, right=0.85, wspace=0)
ax = plt.subplot(gs1[:, :])
ax.tick_params(axis='both', which='major', labelsize=20)
ax.yaxis.set_major_locator(MultipleLocator(60))
h = ax.imshow(U_pred2, interpolation='nearest', cmap='RdBu',
extent=[x.min(), x.max(), t.min(), t.max()],
origin='lower', aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
cax.tick_params(labelsize=20)
fig.colorbar(h, cax=cax, ticks=[5, 10, 15, 20])
ax.plot(X_u_train[:, 0], X_u_train[:, 1], 'kx', markersize=0.8, clip_on=False)
ax.set_ylabel('Time $t$ (s)', fontsize=20)
ax.set_xlabel('Location $x$ (m)', fontsize=20)
ax.legend(frameon=False, loc='best', fontsize=20)
ax.set_title('DL Estimation $v (x,t)$ (m/s)', fontsize=20)
plt.savefig('figures/cav{}_pidl_dl.pdf'.format(N_cav))
plt.savefig('figures/cav{}_pidl_dl.eps'.format(N_cav))
plt.show()
################################# Plot #################################