/
1D_transient.py
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/
1D_transient.py
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import tensorflow as tf
import numpy as np
import scipy.io
import time
import sys
import os
from Utilities.utilities import neural_net, tf_session, mean_squared_error, relative_error, transient_1D_error
os.environ["CUDA_VISIBLE_DEVICES"] = "1"
class PINN(object):
def __init__(self, tau_data, x_data, T_data,
# B.C. && I.C.
tau_U, x_U, T_U,
tau_D, x_D, T_D,
tau_I, x_I, T_I,
layers, batch_size):
# specs
self.layers = layers
self.batch_size = batch_size
# data
[self.tau_data, self.x_data, self.T_data] = [tau_data, x_data, T_data]
[self.tau_U, self.x_U, self.T_U] = [tau_U, x_U, T_U]
[self.tau_D, self.x_D, self.T_D] = [tau_D, x_D, T_D]
[self.tau_I, self.x_I, self.T_I] = [tau_I, x_I, T_I]
# placeholders
[self.tau_data_tf, self.x_data_tf, self.T_data_tf] = \
[tf.placeholder(tf.float32, shape=[None, 1]) for _ in range(3)]
[self.tau_U_tf, self.x_U_tf, self.T_U_tf] = [tf.placeholder(tf.float32, shape=[None, 1]) for _ in range(3)]
[self.tau_D_tf, self.x_D_tf, self.T_D_tf] = [tf.placeholder(tf.float32, shape=[None, 1]) for _ in range(3)]
[self.tau_I_tf, self.x_I_tf, self.T_I_tf] = [tf.placeholder(tf.float32, shape=[None, 1]) for _ in range(3)]
# neural networks
self.net_T = neural_net(self.tau_data, self.x_data, layers=self.layers)
self.T_data_pred = self.net_T(self.tau_data_tf, self.x_data_tf)
# neural networks data at the B.C. && I.C.
self.T_U_pred = self.net_T(self.tau_U_tf, self.x_U_tf)
self.T_D_pred = self.net_T(self.tau_D_tf, self.x_D_tf)
self.T_I_pred = self.net_T(self.tau_I_tf, self.x_I_tf)
self.e_pred = transient_1D_error(self.T_data_pred, self.tau_data_tf, self.x_data_tf)
# loss
self.loss = mean_squared_error(self.T_U_pred, self.T_U_tf) + \
mean_squared_error(self.T_D_pred, self.T_D_tf) + \
mean_squared_error(self.T_I_pred, self.T_I_tf) + \
mean_squared_error(self.e_pred, 0.0)
# optimizers
self.optimizer_LBFGS = tf.contrib.opt.ScipyOptimizerInterface(self.loss,
method='L-BFGS-B',
options={'maxiter': 50000,
'maxfun': 50000,
'maxcor': 50,
'maxls': 50,
'ftol': 1.0 * np.finfo(float).eps})
self.learning_rate = tf.placeholder(tf.float32, shape=[])
self.optimizer = tf.train.AdamOptimizer(learning_rate=self.learning_rate)
self.train_op = self.optimizer.minimize(self.loss)
self.sess = tf_session()
def callback(self, loss):
print('Loss:', loss)
def train(self, total_time, learning_rate):
N_data = self.tau_data.shape[0] # 坐标
start_time = time.time()
begin_time = time.time()
running_time = 0
it = 0
while it < 10000:
if it < 5000:
# for randomly choose data batch
idx_data = np.random.choice(N_data, min(self.batch_size, N_data))
(tau_data_batch,
x_data_batch,
T_data_batch) = (self.tau_data[idx_data, :],
self.x_data[idx_data, :],
self.T_data[idx_data, :])
tf_dict = {self.tau_data_tf: tau_data_batch,
self.x_data_tf: x_data_batch,
self.T_data_tf: T_data_batch,
self.tau_U_tf: self.tau_U,
self.x_U_tf: self.x_U,
self.T_U_tf: self.T_U,
self.tau_D_tf: self.tau_D,
self.x_D_tf: self.x_D,
self.T_D_tf: self.T_D,
self.tau_I_tf: self.tau_I,
self.x_I_tf: self.x_I,
self.T_I_tf: self.T_I,
self.learning_rate: learning_rate}
self.sess.run([self.train_op], tf_dict)
else:
idx_data = np.random.choice(N_data, min(self.batch_size, N_data))
(tau_data_batch,
x_data_batch,
T_data_batch) = (self.tau_data[idx_data, :],
self.x_data[idx_data, :],
self.T_data[idx_data, :])
tf_dict = {self.tau_data_tf: tau_data_batch,
self.x_data_tf: x_data_batch,
self.T_data_tf: T_data_batch,
self.tau_U_tf: self.tau_U,
self.x_U_tf: self.x_U,
self.T_U_tf: self.T_U,
self.tau_D_tf: self.tau_D,
self.x_D_tf: self.x_D,
self.T_D_tf: self.T_D,
self.tau_I_tf: self.tau_I,
self.x_I_tf: self.x_I,
self.T_I_tf: self.T_I,
self.learning_rate: learning_rate}
self.optimizer_LBFGS.minimize(self.sess,
feed_dict = tf_dict,
fetches = [self.loss],
loss_callback = self.callback)
loss_value = self.sess.run(self.loss, tf_dict)
# Print loss
if it % 100 == 0:
elapsed = time.time() - start_time
running_time += elapsed / 3600.0
print('It: %d, Loss: %.3e, Time: %.2fs, Running Time: %.2fh'
% (it, loss_value, elapsed, ((time.time() - begin_time) / 3600)))
sys.stdout.flush()
start_time = time.time()
# f = open("./Results/train_1d.txt", "a") # 记录loss
# f.write("It: {} ".format(it))
# f.write("Loss: {:.3e}\n".format(loss_value))
# print error && save
if it % 1000 == 0:
T_pred = 0 * T_star
T_pred = model.predict(tau_star, x_star)
error_T = relative_error(T_pred, T_star)
print('**************It: %d, Error T: %e**************'
% (it, error_T))
# f = open("./Results/error_1d.txt", "a") # 存error
# f.write("It: {} ".format(it))
# f.write("error_T: {:.3e}\n".format(error_T))
#
# scipy.io.savemat('./Results/Transient1D_results_%s.mat' % (time.strftime('%d_%m_%Y')),
# {'T_pred': T_pred})
# shutdown train
if loss_value <= 6e-5:
break
it += 1
def predict(self, tau_star, x_star):
tf_dict = {self.tau_data_tf: tau_star, self.x_data_tf: x_star}
T_star = self.sess.run(self.T_data_pred, tf_dict)
return T_star
if __name__ == "__main__":
batch_size = 10000
layers = [2] + 10 * [1 * 50] + [1] # input * layers * [output * neurons] * output
# Load Data
data = scipy.io.loadmat('./Data/1d_transient_100.mat')
tau_star = data['tau_star'] # T x 1 (T = N)
x_star = data['x_star'] # N x 1
TAU = tau_star.shape[0]
N = x_star.shape[0]
T_star = data['T_star'] # N x T
# Rearrange Data
TAU_star = np.tile(tau_star, (1, N)).T # N x T
X_star = np.tile(x_star, (1, TAU)) # N x T
tau = TAU_star.flatten()[:, None] # NT x 1
x = X_star.flatten()[:, None] # NT x 1
T = T_star.flatten()[:, None] # NT x 1
######################################################################
######################## Training Data ###############################
######################################################################
TAU_data = TAU # int(sys.argv[1])
N_data = N # int(sys.argv[2])
idx_tau = np.concatenate([np.array([0]), np.random.choice(TAU - 2, TAU_data - 2, replace=False) + 1, np.array([TAU - 1])])
idx_x = np.random.choice(N, N_data, replace=False)
tau_data = TAU_star[:, idx_tau][idx_x, :].flatten()[: , None]
x_data = X_star[:, idx_tau][idx_x, :].flatten()[: , None]
T_data = T_star[:, idx_tau][idx_x, :].flatten()[: , None]
# Training Data on B.C. && I.C.
tau_U = tau[x == x.max()][:, None]
x_U = x[x == x.max()][:, None]
T_U = T[x == x.max()][:, None]
tau_D = tau[x == x.min()][:, None]
x_D = x[x == x.min()][:, None]
T_D = T[x == x.min()][:, None]
tau_I = tau[tau == tau.min()][:, None]
x_I = x[tau == tau.min()][:, None]
T_I = T[tau == tau.min()][:, None]
# Training
model = PINN(tau_data, x_data, T_data,
tau_U, x_U, T_U,
tau_D, x_D, T_D,
tau_I, x_I, T_I,
layers, batch_size)
model.train(total_time=20, learning_rate=1e-3)
################# Save Data ###########################
T_pred = 0 * T_star
# Prediction
T_pred = model.predict(tau_star, x_star)
# Error
error_T = relative_error(T_pred, T_star)
print('Error T: %e' % (error_T))
# f = open("./Results/error_1d.txt", "a") # 存error
#
# f.write("error_T: {:.3e}".format(error_T))
#
# scipy.io.savemat('./Results/Transient1D_results_%s.mat' % (time.strftime('%d_%m_%Y')), {'T_pred': T_pred})