def solve_Multiscale_PDE(R):
log_out_path = R['FolderName'] # 将路径从字典 R 中提取出来
if not os.path.exists(log_out_path): # 判断路径是否已经存在
os.mkdir(log_out_path) # 无 log_out_path 路径，创建一个 log_out_path 路径
outfile_name1 = '%s%s.txt' % ('log2', 'train')
log_fileout_NN = open(os.path.join(log_out_path, outfile_name1),
'w') # 在这个路径下创建并打开一个可写的 log_train.txt文件
dictionary_out2file(R,
log_fileout_NN,
actName2normal=R['act_name2NN1'],
actName2scale=R['act_name2NN2'])
# laplace 问题需要的设置
batchsize_it = R['batch_size2interior']
batchsize_bd = R['batch_size2boundary']
bd_penalty_init = R[
'init_boundary_penalty'] # Regularization parameter for boundary conditions
lr_decay = R['learning_rate_decay']
learning_rate = R['learning_rate']
init_penalty2powU = R['balance2solus']
hidden2normal = R['hidden2normal']
hidden2scale = R['hidden2scale']
wb_regular = R[
'regular_weight_biases'] # Regularization parameter for weights and biases
# ------- set the problem ---------
input_dim = R['input_dim']
out_dim = R['output_dim']
act_func1 = R['act_name2NN1']
act_func2 = R['act_name2NN2']
region_l = 0.0
region_r = 1.0
if R['PDE_type'] == 'general_laplace':
# -laplace u = f
region_l = 0.0
region_r = 1.0
f, u_true, u_left, u_right = laplace_eqs1d.get_laplace_infos(
input_dim=input_dim,
out_dim=out_dim,
left_bottom=region_l,
right_top=region_r,
laplace_name=R['equa_name'])
elif R['PDE_type'] == 'p_laplace':
# 求解如下方程, A_eps(x) 震荡的比较厉害，具有多个尺度
# d **** d ****
# - ---- | A_eps(x)* ---- u_eps(x) | =f(x), x \in R^n
# dx **** dx ****
# 问题区域，每个方向设置为一样的长度。等网格划分，对于二维是方形区域
p_index = R['order2laplace']
epsilon = R['epsilon']
if 2 == p_index:
region_l = 0.0
region_r = 1.0
u_true, f, A_eps, u_left, u_right = pLaplace_eqs1d.get_infos_2laplace(
in_dim=input_dim,
out_dim=out_dim,
region_a=region_l,
region_b=region_r,
p=p_index,
eps=epsilon)
elif 3 == p_index:
region_l = 0.0
region_r = 1.0
u_true, f, A_eps, u_left, u_right = pLaplace_eqs1d.get_infos_3laplace(
in_dim=input_dim,
out_dim=out_dim,
region_a=region_l,
region_b=region_r,
p=p_index,
eps=epsilon)
elif 5 == p_index:
region_l = 0.0
region_r = 1.0
u_true, f, A_eps, u_left, u_right = pLaplace_eqs1d.get_infos_5laplace(
in_dim=input_dim,
out_dim=out_dim,
region_a=region_l,
region_b=region_r,
p=p_index,
eps=epsilon)
elif 8 == p_index:
region_l = 0.0
region_r = 1.0
u_true, f, A_eps, u_left, u_right = pLaplace_eqs1d.get_infos_8laplace(
in_dim=input_dim,
out_dim=out_dim,
region_a=region_l,
region_b=region_r,
p=p_index,
eps=epsilon)
else:
region_l = 0.0
region_r = 1.0
u_true, f, A_eps, u_left, u_right = pLaplace_eqs1d.get_infos_pLaplace(
in_dim=input_dim,
out_dim=out_dim,
region_a=region_l,
region_b=region_r,
p=p_index,
eps=epsilon,
eqs_name=R['equa_name'])
# 初始化权重和和偏置的模式
if R['weight_biases_model'] == 'general_model':
flag_normal = 'WB_NN2normal'
flag_scale = 'WB_NN2scale'
# Weights, Biases = PDE_DNN_base.Initial_DNN2different_hidden(input_dim, out_dim, hidden_layers, flag)
# Weights, Biases = laplace_DNN1d_base.initialize_NN_xavier(input_dim, out_dim, hidden_layers, flag1)
# Weights, Biases = laplace_DNN1d_base.initialize_NN_random_normal(input_dim, out_dim, hidden_layers, flag1)
if R['model2normal'] == 'PDE_DNN_Cos_C_Sin_Base' or R[
'model2normal'] == 'DNN_adaptCosSin_Base':
W2NN_Normal, B2NN_Normal = DNN_base.initialize_NN_random_normal2_CS(
input_dim, out_dim, hidden2normal, flag_normal)
else:
W2NN_Normal, B2NN_Normal = DNN_base.initialize_NN_random_normal2(
input_dim, out_dim, hidden2normal, flag_normal)
if R['model2scale'] == 'PDE_DNN_Cos_C_Sin_Base' or R[
'model2scale'] == 'DNN_adaptCosSin_Base':
W2NN_freqs, B2NN_freqs = DNN_base.initialize_NN_random_normal2_CS(
input_dim, out_dim, hidden2scale, flag_scale)
else:
W2NN_freqs, B2NN_freqs = DNN_base.initialize_NN_random_normal2(
input_dim, out_dim, hidden2scale, flag_scale)
global_steps = tf.Variable(0, trainable=False)
with tf.device('/gpu:%s' % (R['gpuNo'])):
with tf.variable_scope('vscope', reuse=tf.AUTO_REUSE):
X_it = tf.placeholder(tf.float32,
name='X_it',
shape=[None, input_dim]) # * 行 1 列
X_left_bd = tf.placeholder(tf.float32,
name='X_left_bd',
shape=[None, input_dim]) # * 行 1 列
X_right_bd = tf.placeholder(tf.float32,
name='X_right_bd',
shape=[None, input_dim]) # * 行 1 列
bd_penalty = tf.placeholder_with_default(input=1e3,
shape=[],
name='bd_p')
penalty2powU = tf.placeholder_with_default(input=1.0,
shape=[],
name='p_powU')
in_learning_rate = tf.placeholder_with_default(input=1e-5,
shape=[],
name='lr')
train_opt = tf.placeholder_with_default(input=True,
shape=[],
name='train_opt')
if R['model2normal'] == 'PDE_DNN':
U_NN_Normal = DNN_base.PDE_DNN(X_it,
W2NN_Normal,
B2NN_Normal,
hidden2normal,
activate_name=act_func1)
ULeft_NN_Normal = DNN_base.PDE_DNN(X_left_bd,
W2NN_Normal,
B2NN_Normal,
hidden2normal,
activate_name=act_func1)
URight_NN_Normal = DNN_base.PDE_DNN(X_right_bd,
W2NN_Normal,
B2NN_Normal,
hidden2normal,
activate_name=act_func1)
elif R['model2normal'] == 'PDE_DNN_Cos_C_Sin_Base':
freq = [1]
U_NN_Normal = DNN_base.PDE_DNN_Cos_C_Sin_Base(
X_it,
W2NN_Normal,
B2NN_Normal,
hidden2normal,
freq,
activate_name=act_func1)
ULeft_NN_Normal = DNN_base.PDE_DNN_Cos_C_Sin_Base(
X_left_bd,
W2NN_Normal,
B2NN_Normal,
hidden2normal,
freq,
activate_name=act_func1)
URight_NN_Normal = DNN_base.PDE_DNN_Cos_C_Sin_Base(
X_right_bd,
W2NN_Normal,
B2NN_Normal,
hidden2normal,
freq,
activate_name=act_func1)
elif R['model2normal'] == 'DNN_adaptCosSin_Base':
freq = [1]
U_NN_Normal = DNN_base.DNN_adaptCosSin_Base(
X_it,
W2NN_Normal,
B2NN_Normal,
hidden2normal,
freq,
activate_name=act_func1)
ULeft_NN_Normal = DNN_base.DNN_adaptCosSin_Base(
X_left_bd,
W2NN_Normal,
B2NN_Normal,
hidden2normal,
freq,
activate_name=act_func1)
URight_NN_Normal = DNN_base.DNN_adaptCosSin_Base(
X_right_bd,
W2NN_Normal,
B2NN_Normal,
hidden2normal,
freq,
activate_name=act_func1)
freqs = R['freqs']
if R['model2scale'] == 'PDE_DNN_scale':
U_NN_freqs = DNN_base.PDE_DNN_scale(X_it,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
ULeft_NN_freqs = DNN_base.PDE_DNN_scale(
X_left_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
URight_NN_freqs = DNN_base.PDE_DNN_scale(
X_right_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
elif R['model2scale'] == 'PDE_DNN_adapt_scale':
U_NN_freqs = DNN_base.PDE_DNN_adapt_scale(
X_it,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
ULeft_NN_freqs = DNN_base.PDE_DNN_adapt_scale(
X_left_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
URight_NN_freqs = DNN_base.PDE_DNN_adapt_scale(
X_right_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
elif R['model2scale'] == 'PDE_DNN_FourierBase':
U_NN_freqs = DNN_base.PDE_DNN_FourierBase(
X_it,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
ULeft_NN_freqs = DNN_base.PDE_DNN_FourierBase(
X_left_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
URight_NN_freqs = DNN_base.PDE_DNN_FourierBase(
X_right_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
elif R['model2scale'] == 'PDE_DNN_Cos_C_Sin_Base':
U_NN_freqs = DNN_base.PDE_DNN_Cos_C_Sin_Base(
X_it,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
ULeft_NN_freqs = DNN_base.PDE_DNN_Cos_C_Sin_Base(
X_left_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
URight_NN_freqs = DNN_base.PDE_DNN_Cos_C_Sin_Base(
X_right_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
elif R['model2scale'] == 'DNN_adaptCosSin_Base':
U_NN_freqs = DNN_base.DNN_adaptCosSin_Base(
X_it,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
ULeft_NN_freqs = DNN_base.DNN_adaptCosSin_Base(
X_left_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
URight_NN_freqs = DNN_base.DNN_adaptCosSin_Base(
X_right_bd,
W2NN_freqs,
B2NN_freqs,
hidden2scale,
freqs,
activate_name=act_func2)
U_NN = U_NN_Normal + U_NN_freqs
# 变分形式的loss of interior，训练得到的 U_NN1 是 * 行 1 列, 因为 一个点对(x,y) 得到一个 u 值
dU_NN_Normal = tf.gradients(U_NN_Normal, X_it)[0] # * 行 2 列
dU_NN_freqs = tf.gradients(U_NN_freqs, X_it)[0] # * 行 2 列
if R['variational_loss'] == 1:
dU_NN = tf.add(dU_NN_Normal, dU_NN_freqs)
if R['PDE_type'] == 'general_laplace':
laplace_norm2NN = tf.reduce_sum(tf.square(dU_NN), axis=-1)
loss_it_NN = (1.0 / 2) * tf.reshape(laplace_norm2NN, shape=[-1, 1]) - \
tf.multiply(tf.reshape(f(X_it), shape=[-1, 1]), U_NN)
elif R['PDE_type'] == 'p_laplace':
# a_eps = A_eps(X_it) # * 行 1 列
a_eps = 1 / (2 + tf.cos(2 * np.pi * X_it / epsilon))
laplace_p_pow2NN = tf.reduce_sum(
a_eps * tf.pow(tf.abs(dU_NN), p_index), axis=-1)
loss_it_NN = (1.0 / p_index) * tf.reshape(laplace_p_pow2NN, shape=[-1, 1]) - \
tf.multiply(tf.reshape(f(X_it), shape=[-1, 1]), U_NN)
Loss_it2NN = tf.reduce_mean(loss_it_NN) * (region_r - region_l)
if R['wavelet'] == 1:
# |Uc*Uf|^2-->0
norm2UdU = tf.square(tf.multiply(U_NN_Normal, U_NN_freqs))
UNN_dot_UNN = tf.reduce_mean(norm2UdU, axis=0)
elif R['wavelet'] == 2:
# |a(x)*(grad Uc)*(grad Uf)|^2-->0
dU_dot_dU = tf.multiply(dU_NN_Normal, dU_NN_freqs)
sum2dUdU = tf.reshape(tf.reduce_sum(dU_dot_dU, axis=-1),
shape=[-1, 1])
norm2AdUdU = tf.square(tf.multiply(a_eps, sum2dUdU))
# norm2AdUdU = tf.square(sum2dUdU)
UNN_dot_UNN = tf.reduce_mean(norm2AdUdU, axis=0)
else:
U_dot_U = tf.reduce_mean(tf.square(
tf.multiply(U_NN_Normal, U_NN_freqs)),
axis=0)
dU_dot_dU = tf.multiply(dU_NN_Normal, dU_NN_freqs)
sum2dUdU = tf.reshape(tf.reduce_sum(dU_dot_dU, axis=-1),
shape=[-1, 1])
norm2AdUdU = tf.square(tf.multiply(a_eps, sum2dUdU))
UNN_dot_UNN = tf.reduce_mean(norm2AdUdU, axis=0) + U_dot_U
elif R['variational_loss'] == 2:
dU_NN = tf.add(dU_NN_Normal, dU_NN_freqs)
if R['PDE_type'] == 'general_laplace':
laplace_norm2NN = tf.reduce_sum(tf.square(dU_NN), axis=-1)
loss_it_NN = (1.0 / 2) * tf.reshape(laplace_norm2NN, shape=[-1, 1]) - \
tf.multiply(tf.reshape(f(X_it), shape=[-1, 1]), U_NN)
elif R['PDE_type'] == 'p_laplace':
# a_eps = A_eps(X_it) # * 行 1 列
a_eps = 1 / (2 + tf.cos(2 * np.pi * X_it / epsilon))
laplace_p_pow2NN = tf.reduce_sum(
a_eps * tf.pow(tf.abs(dU_NN), p_index), axis=-1)
loss_it_NN = (1.0 / p_index) * tf.reshape(laplace_p_pow2NN, shape=[-1, 1]) - \
tf.multiply(tf.reshape(f(X_it), shape=[-1, 1]), U_NN)
Loss_it2NN = tf.reduce_mean(loss_it_NN) * (region_r - region_l)
if R['wavelet'] == 1:
norm2UdU = tf.square(tf.multiply(U_NN_Normal, U_NN_freqs))
UNN_dot_UNN = tf.reduce_mean(norm2UdU, axis=0)
else:
UNN_dot_UNN = tf.constant(0.0)
Loss2UNN_dot_UNN = penalty2powU * UNN_dot_UNN
U_left = tf.reshape(u_left(X_left_bd), shape=[-1, 1])
U_right = tf.reshape(u_right(X_right_bd), shape=[-1, 1])
loss_bd_Normal = tf.square(ULeft_NN_Normal -
U_left) + tf.square(URight_NN_Normal -
U_right)
loss_bd_Freqs = tf.square(ULeft_NN_freqs -
U_left) + tf.square(URight_NN_freqs -
U_right)
Loss_bd2NN = tf.reduce_mean(loss_bd_Normal) + tf.reduce_mean(
loss_bd_Freqs)
if R['regular_weight_model'] == 'L1':
regular_WB_Normal = DNN_base.regular_weights_biases_L1(
W2NN_Normal, B2NN_Normal) # 正则化权重和偏置 L1正则化
regular_WB_Scale = DNN_base.regular_weights_biases_L1(
W2NN_freqs, B2NN_freqs) # 正则化权重和偏置 L1正则化
elif R['regular_weight_model'] == 'L2':
regular_WB_Normal = DNN_base.regular_weights_biases_L2(
W2NN_Normal, B2NN_Normal) # 正则化权重和偏置 L2正则化
regular_WB_Scale = DNN_base.regular_weights_biases_L2(
W2NN_freqs, B2NN_freqs) # 正则化权重和偏置 L2正则化
else:
regular_WB_Normal = tf.constant(0.0) # 无正则化权重参数
regular_WB_Scale = tf.constant(0.0)
penalty_Weigth_Bias = wb_regular * (regular_WB_Normal +
regular_WB_Scale)
Loss2NN = Loss_it2NN + bd_penalty * Loss_bd2NN + Loss2UNN_dot_UNN + penalty_Weigth_Bias
my_optimizer = tf.train.AdamOptimizer(in_learning_rate)
if R['variational_loss'] == 1:
if R['train_group'] == 1:
train_op1 = my_optimizer.minimize(Loss_it2NN,
global_step=global_steps)
train_op2 = my_optimizer.minimize(Loss_bd2NN,
global_step=global_steps)
train_op3 = my_optimizer.minimize(Loss2UNN_dot_UNN,
global_step=global_steps)
train_op4 = my_optimizer.minimize(Loss2NN,
global_step=global_steps)
train_Loss2NN = tf.group(train_op1, train_op2, train_op3,
train_op4)
elif R['train_group'] == 2:
train_op1 = my_optimizer.minimize(Loss2NN,
global_step=global_steps)
train_op2 = my_optimizer.minimize(Loss_bd2NN,
global_step=global_steps)
train_op3 = my_optimizer.minimize(Loss2UNN_dot_UNN,
global_step=global_steps)
train_Loss2NN = tf.group(train_op1, train_op2, train_op3)
else:
train_Loss2NN = my_optimizer.minimize(
Loss2NN, global_step=global_steps)
elif R['variational_loss'] == 2:
if R['train_group'] == 1:
train_op1 = my_optimizer.minimize(Loss_it2NN,
global_step=global_steps)
train_op2 = my_optimizer.minimize(Loss_bd2NN,
global_step=global_steps)
train_op3 = my_optimizer.minimize(Loss2NN,
global_step=global_steps)
train_Loss2NN = tf.group(train_op1, train_op2, train_op3)
elif R['train_group'] == 2:
train_op1 = my_optimizer.minimize(Loss2NN,
global_step=global_steps)
train_op2 = my_optimizer.minimize(Loss_bd2NN,
global_step=global_steps)
train_Loss2NN = tf.group(train_op1, train_op2)
else:
train_Loss2NN = my_optimizer.minimize(
Loss2NN, global_step=global_steps)
# 训练上的真解值和训练结果的误差
U_true = u_true(X_it)
train_mse_NN = tf.reduce_mean(tf.square(U_true - U_NN))
train_rel_NN = train_mse_NN / tf.reduce_mean(tf.square(U_true))
t0 = time.time()
# 空列表, 使用 append() 添加元素
lossIt_all2NN, lossBD_all2NN, loss_all2NN, UDU_NN, train_mse_all2NN, train_rel_all2NN = [], [], [], [], [], []
test_mse_all2NN, test_rel_all2NN = [], []
test_epoch = []
test_batch_size = 1000
test_x_bach = np.reshape(
np.linspace(region_l, region_r, num=test_batch_size), [-1, 1])
saveData.save_testData_or_solus2mat(test_x_bach,
dataName='testx',
outPath=R['FolderName'])
# ConfigProto 加上allow_soft_placement=True就可以使用 gpu 了
config = tf.ConfigProto(allow_soft_placement=True) # 创建sess的时候对sess进行参数配置
config.gpu_options.allow_growth = True # True是让TensorFlow在运行过程中动态申请显存，避免过多的显存占用。
config.allow_soft_placement = True # 当指定的设备不存在时，允许选择一个存在的设备运行。比如gpu不存在，自动降到cpu上运行
with tf.Session(config=config) as sess:
sess.run(tf.global_variables_initializer())
tmp_lr = learning_rate
for i_epoch in range(R['max_epoch'] + 1):
x_it_batch = DNN_data.rand_it(batchsize_it,
input_dim,
region_a=region_l,
region_b=region_r)
xl_bd_batch, xr_bd_batch = DNN_data.rand_bd_1D(batchsize_bd,
input_dim,
region_a=region_l,
region_b=region_r)
tmp_lr = tmp_lr * (1 - lr_decay)
if R['activate_penalty2bd_increase'] == 1:
if i_epoch < int(R['max_epoch'] / 10):
temp_penalty_bd = bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 5):
temp_penalty_bd = 10 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 4):
temp_penalty_bd = 50 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 2):
temp_penalty_bd = 100 * bd_penalty_init
elif i_epoch < int(3 * R['max_epoch'] / 4):
temp_penalty_bd = 200 * bd_penalty_init
else:
temp_penalty_bd = 500 * bd_penalty_init
elif R['activate_penalty2bd_increase'] == 2:
if i_epoch < int(R['max_epoch'] / 10):
temp_penalty_bd = 5 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 5):
temp_penalty_bd = 1 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 4):
temp_penalty_bd = 0.5 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 2):
temp_penalty_bd = 0.1 * bd_penalty_init
elif i_epoch < int(3 * R['max_epoch'] / 4):
temp_penalty_bd = 0.05 * bd_penalty_init
else:
temp_penalty_bd = 0.02 * bd_penalty_init
else:
temp_penalty_bd = bd_penalty_init
if R['activate_powSolus_increase'] == 1:
if i_epoch < int(R['max_epoch'] / 10):
temp_penalty_powU = init_penalty2powU
elif i_epoch < int(R['max_epoch'] / 5):
temp_penalty_powU = 10 * init_penalty2powU
elif i_epoch < int(R['max_epoch'] / 4):
temp_penalty_powU = 50 * init_penalty2powU
elif i_epoch < int(R['max_epoch'] / 2):
temp_penalty_powU = 100 * init_penalty2powU
elif i_epoch < int(3 * R['max_epoch'] / 4):
temp_penalty_powU = 200 * init_penalty2powU
else:
temp_penalty_powU = 500 * init_penalty2powU
elif R['activate_powSolus_increase'] == 2:
if i_epoch < int(R['max_epoch'] / 10):
temp_penalty_powU = 5 * init_penalty2powU
elif i_epoch < int(R['max_epoch'] / 5):
temp_penalty_powU = 1 * init_penalty2powU
elif i_epoch < int(R['max_epoch'] / 4):
temp_penalty_powU = 0.5 * init_penalty2powU
elif i_epoch < int(R['max_epoch'] / 2):
temp_penalty_powU = 0.1 * init_penalty2powU
elif i_epoch < int(3 * R['max_epoch'] / 4):
temp_penalty_powU = 0.05 * init_penalty2powU
else:
temp_penalty_powU = 0.02 * init_penalty2powU
else:
temp_penalty_powU = init_penalty2powU
p_WB = 0.0
_, loss_it_nn, loss_bd_nn, loss_nn, udu_nn, train_mse_nn, train_rel_nn = sess.run(
[
train_Loss2NN, Loss_it2NN, Loss_bd2NN, Loss2NN,
UNN_dot_UNN, train_mse_NN, train_rel_NN
],
feed_dict={
X_it: x_it_batch,
X_left_bd: xl_bd_batch,
X_right_bd: xr_bd_batch,
in_learning_rate: tmp_lr,
bd_penalty: temp_penalty_bd,
penalty2powU: temp_penalty_powU
})
lossIt_all2NN.append(loss_it_nn)
lossBD_all2NN.append(loss_bd_nn)
loss_all2NN.append(loss_nn)
UDU_NN.append(udu_nn)
train_mse_all2NN.append(train_mse_nn)
train_rel_all2NN.append(train_rel_nn)
if i_epoch % 1000 == 0:
run_times = time.time() - t0
DNN_tools.print_and_log_train_one_epoch(i_epoch,
run_times,
tmp_lr,
temp_penalty_bd,
temp_penalty_powU,
p_WB,
loss_it_nn,
loss_bd_nn,
loss_nn,
udu_nn,
train_mse_nn,
train_rel_nn,
log_out=log_fileout_NN)
# --------------------------- test network ----------------------------------------------
test_epoch.append(i_epoch / 1000)
train_option = False
u_true2test, utest_nn, u_nn_normal, u_nn_scale = sess.run(
[U_true, U_NN, U_NN_Normal, U_NN_freqs],
feed_dict={
X_it: test_x_bach,
train_opt: train_option
})
test_mse2nn = np.mean(np.square(u_true2test - utest_nn))
test_mse_all2NN.append(test_mse2nn)
test_rel2nn = test_mse2nn / np.mean(np.square(u_true2test))
test_rel_all2NN.append(test_rel2nn)
DNN_tools.print_and_log_test_one_epoch(test_mse2nn,
test_rel2nn,
log_out=log_fileout_NN)
# ----------------------- save training results to mat files, then plot them ---------------------------------
saveData.save_trainLoss2mat_1actFunc(lossIt_all2NN,
lossBD_all2NN,
loss_all2NN,
actName=act_func1,
outPath=R['FolderName'])
saveData.save_train_MSE_REL2mat(train_mse_all2NN,
train_rel_all2NN,
actName=act_func1,
outPath=R['FolderName'])
plotData.plotTrain_loss_1act_func(lossIt_all2NN,
lossType='loss_it',
seedNo=R['seed'],
outPath=R['FolderName'])
plotData.plotTrain_loss_1act_func(lossBD_all2NN,
lossType='loss_bd',
seedNo=R['seed'],
outPath=R['FolderName'],
yaxis_scale=True)
plotData.plotTrain_loss_1act_func(loss_all2NN,
lossType='loss',
seedNo=R['seed'],
outPath=R['FolderName'])
plotData.plotTrain_MSE_REL_1act_func(train_mse_all2NN,
train_rel_all2NN,
actName=act_func2,
seedNo=R['seed'],
outPath=R['FolderName'],
yaxis_scale=True)
# ---------------------- save testing results to mat files, then plot them --------------------------------
saveData.save_testData_or_solus2mat(u_true2test,
dataName='Utrue',
outPath=R['FolderName'])
saveData.save_testData_or_solus2mat(utest_nn,
dataName=act_func1,
outPath=R['FolderName'])
saveData.save_testData_or_solus2mat(u_nn_normal,
dataName='normal',
outPath=R['FolderName'])
saveData.save_testData_or_solus2mat(u_nn_scale,
dataName='scale',
outPath=R['FolderName'])
saveData.save_testMSE_REL2mat(test_mse_all2NN,
test_rel_all2NN,
actName=act_func2,
outPath=R['FolderName'])
plotData.plotTest_MSE_REL(test_mse_all2NN,
test_rel_all2NN,
test_epoch,
actName=act_func2,
seedNo=R['seed'],
outPath=R['FolderName'],
yaxis_scale=True)
def solve_Multiscale_PDE(R):
log_out_path = R['FolderName'] # 将路径从字典 R 中提取出来
if not os.path.exists(log_out_path): # 判断路径是否已经存在
os.mkdir(log_out_path) # 无 log_out_path 路径，创建一个 log_out_path 路径
logfile_name = '%s_%s.txt' % ('log2train', R['name2act_hidden'])
log_fileout = open(os.path.join(log_out_path, logfile_name), 'w') # 在这个路径下创建并打开一个可写的 log_train.txt文件
DNN_Log_Print.dictionary_out2file(R, log_fileout)
# 问题需要的设置
batchsize_it = R['batch_size2interior']
batchsize_bd = R['batch_size2boundary']
bd_penalty_init = R['init_boundary_penalty'] # Regularization parameter for boundary conditions
penalty2WB = R['penalty2weight_biases'] # Regularization parameter for weights and biases
lr_decay = R['learning_rate_decay']
learning_rate = R['learning_rate']
hidden_layers = R['hidden_layers']
actIn_func = R['name2act_in']
act_func = R['name2act_hidden']
actOut_func = R['name2act_out']
input_dim = R['input_dim']
out_dim = R['output_dim']
lambda2lncosh = R['lambda2lncosh']
# pLaplace 算子需要的额外设置, 先预设一下
p_index = 2
epsilon = 0.1
mesh_number = 2
region_lb = 0.0
region_rt = 1.0
if R['PDE_type'] == 'general_Laplace':
# -laplace u = f
region_lb = 0.0
region_rt = 1.0
f, u_true, u_left, u_right, u_bottom, u_top = General_Laplace.get_infos2Laplace_2D(
input_dim=input_dim, out_dim=out_dim, left_bottom=region_lb, right_top=region_rt, equa_name=R['equa_name'])
elif R['PDE_type'] == 'pLaplace_implicit':
p_index = R['order2pLaplace_operator']
epsilon = R['epsilon']
mesh_number = R['mesh_number']
if R['equa_name'] == 'multi_scale2D_5':
region_lb = 0.0
region_rt = 1.0
else:
region_lb = -1.0
region_rt = 1.0
u_true, f, A_eps, u_left, u_right, u_bottom, u_top = MS_LaplaceEqs.get_infos2pLaplace_2D(
input_dim=input_dim, out_dim=out_dim, mesh_number=R['mesh_number'], intervalL=0.0, intervalR=1.0,
equa_name=R['equa_name'])
elif R['PDE_type'] == 'pLaplace_explicit':
p_index = R['order2pLaplace_operator']
epsilon = R['epsilon']
mesh_number = R['mesh_number']
if R['equa_name'] == 'multi_scale2D_7':
region_lb = 0.0
region_rt = 1.0
u_true = MS_LaplaceEqs.true_solution2E7(input_dim, out_dim, eps=epsilon)
u_left, u_right, u_bottom, u_top = MS_LaplaceEqs.boundary2E7(
input_dim, out_dim, region_lb, region_rt, eps=epsilon)
A_eps = MS_LaplaceEqs.elliptic_coef2E7(input_dim, out_dim, eps=epsilon)
elif R['PDE_type'] == 'Possion_Boltzmann':
# 求解如下方程, A_eps(x) 震荡的比较厉害，具有多个尺度
# d **** d ****
# - ---- | A_eps(x)* ---- u_eps(x) | + Ku_eps =f(x), x \in R^n
# dx **** dx ****
# region_lb = -1.0
region_lb = 0.0
region_rt = 1.0
p_index = R['order2pLaplace_operator']
epsilon = R['epsilon']
mesh_number = R['mesh_number']
A_eps, kappa, u_true, u_left, u_right, u_top, u_bottom, f = MS_BoltzmannEqs.get_infos2Boltzmann_2D(
equa_name=R['equa_name'], intervalL=region_lb, intervalR=region_rt)
elif R['PDE_type'] == 'Convection_diffusion':
region_lb = -1.0
region_rt = 1.0
p_index = R['order2pLaplace_operator']
epsilon = R['epsilon']
mesh_number = R['mesh_number']
A_eps, Bx, By, u_true, u_left, u_right, u_top, u_bottom, f = MS_ConvectionEqs.get_infos2Convection_2D(
equa_name=R['equa_name'], eps=epsilon, region_lb=0.0, region_rt=1.0)
# 初始化权重和和偏置
flag1 = 'WB'
if R['model2NN'] == 'DNN_FourierBase':
W2NN, B2NN = DNN_base.Xavier_init_NN_Fourier(input_dim, out_dim, hidden_layers, flag1)
else:
W2NN, B2NN = DNN_base.Xavier_init_NN(input_dim, out_dim, hidden_layers, flag1)
global_steps = tf.compat.v1.Variable(0, trainable=False)
with tf.device('/gpu:%s' % (R['gpuNo'])):
with tf.compat.v1.variable_scope('vscope', reuse=tf.compat.v1.AUTO_REUSE):
XY_it = tf.compat.v1.placeholder(tf.float32, name='X_it', shape=[None, input_dim]) # * 行 2 列
XY_left = tf.compat.v1.placeholder(tf.float32, name='X_left_bd', shape=[None, input_dim]) # * 行 2 列
XY_right = tf.compat.v1.placeholder(tf.float32, name='X_right_bd', shape=[None, input_dim]) # * 行 2 列
XY_bottom = tf.compat.v1.placeholder(tf.float32, name='Y_bottom_bd', shape=[None, input_dim]) # * 行 2 列
XY_top = tf.compat.v1.placeholder(tf.float32, name='Y_top_bd', shape=[None, input_dim]) # * 行 2 列
boundary_penalty = tf.compat.v1.placeholder_with_default(input=1e3, shape=[], name='bd_p')
in_learning_rate = tf.compat.v1.placeholder_with_default(input=1e-5, shape=[], name='lr')
# 供选择的网络模式
if R['model2NN'] == 'DNN':
UNN = DNN_base.DNN(XY_it, W2NN, B2NN, hidden_layers, activateIn_name=actIn_func, activate_name=act_func,
activateOut_name=actOut_func)
UNN_left = DNN_base.DNN(XY_left, W2NN, B2NN, hidden_layers, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_right = DNN_base.DNN(XY_right, W2NN, B2NN, hidden_layers, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_bottom = DNN_base.DNN(XY_bottom, W2NN, B2NN, hidden_layers, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_top = DNN_base.DNN(XY_top, W2NN, B2NN, hidden_layers, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
elif R['model2NN'] == 'DNN_scale':
freq = R['freq']
UNN = DNN_base.DNN_scale(XY_it, W2NN, B2NN, hidden_layers, freq, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_left = DNN_base.DNN_scale(XY_left, W2NN, B2NN, hidden_layers, freq, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_right = DNN_base.DNN_scale(XY_right, W2NN, B2NN, hidden_layers, freq, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_bottom = DNN_base.DNN_scale(XY_bottom, W2NN, B2NN, hidden_layers, freq, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_top = DNN_base.DNN_scale(XY_top, W2NN, B2NN, hidden_layers, freq, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
elif R['model2NN'] == 'DNN_adapt_scale':
freqs = R['freq']
UNN = DNN_base.DNN_adapt_scale(XY_it, W2NN, B2NN, hidden_layers, freqs, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_left = DNN_base.DNN_adapt_scale(XY_left, W2NN, B2NN, hidden_layers, freqs, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_right = DNN_base.DNN_adapt_scale(XY_right, W2NN, B2NN, hidden_layers, freqs, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_bottom = DNN_base.DNN_adapt_scale(XY_bottom, W2NN, B2NN, hidden_layers, freqs, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
UNN_top = DNN_base.DNN_adapt_scale(XY_top, W2NN, B2NN, hidden_layers, freqs, activateIn_name=actIn_func,
activate_name=act_func, activateOut_name=actOut_func)
elif R['model2NN'] == 'DNN_FourierBase':
freqs = R['freq']
UNN = DNN_base.DNN_FourierBase(XY_it, W2NN, B2NN, hidden_layers, freqs, activate_name=act_func,
activateOut_name=actOut_func, sFourier=R['sfourier'])
UNN_left = DNN_base.DNN_FourierBase(XY_left, W2NN, B2NN, hidden_layers, freqs, activate_name=act_func,
activateOut_name=actOut_func, sFourier=R['sfourier'])
UNN_right = DNN_base.DNN_FourierBase(XY_right, W2NN, B2NN, hidden_layers, freqs, activate_name=act_func,
activateOut_name=actOut_func, sFourier=R['sfourier'])
UNN_bottom = DNN_base.DNN_FourierBase(XY_bottom, W2NN, B2NN, hidden_layers, freqs, activate_name=act_func,
activateOut_name=actOut_func, sFourier=R['sfourier'])
UNN_top = DNN_base.DNN_FourierBase(XY_top, W2NN, B2NN, hidden_layers, freqs, activate_name=act_func,
activateOut_name=actOut_func, sFourier=R['sfourier'])
X_it = tf.reshape(XY_it[:, 0], shape=[-1, 1])
Y_it = tf.reshape(XY_it[:, 1], shape=[-1, 1])
# 变分形式的loss of interior，训练得到的 UNN 是 * 行 1 列
if R['loss_type'] == 'variational_loss':
dUNN = tf.gradients(UNN, XY_it)[0] # * 行 2 列
dUNN_Norm = tf.reshape(tf.sqrt(tf.reduce_sum(tf.square(dUNN), axis=-1)), shape=[-1, 1]) # 按行求和
if R['PDE_type'] == 'general_Laplace':
dUNN_2Norm = tf.square(dUNN_Norm)
loss_it_variational = (1.0 / 2) * dUNN_2Norm - \
tf.multiply(tf.reshape(f(X_it, Y_it), shape=[-1, 1]), UNN)
elif R['PDE_type'] == 'pLaplace_explicit' or R['PDE_type'] == 'pLaplace_implicit':
a_eps = A_eps(X_it, Y_it) # * 行 1 列
AdUNN_pNorm = tf.multiply(a_eps, tf.pow(dUNN_Norm, p_index))
if R['equa_name'] == 'multi_scale2D_7':
fxy = MS_LaplaceEqs.get_force_side2MS_E7(x=X_it, y=Y_it)
loss_it_variational = (1.0 / p_index) * AdUNN_pNorm - \
tf.multiply(tf.reshape(fxy, shape=[-1, 1]), UNN)
else:
loss_it_variational = (1.0 / p_index) * AdUNN_pNorm - \
tf.multiply(tf.reshape(f(X_it, Y_it), shape=[-1, 1]), UNN)
elif R['PDE_type'] == 'Possion_Boltzmann':
a_eps = A_eps(X_it, Y_it) # * 行 1 列
Kappa = kappa(X_it, Y_it) # * 行 1 列
AdUNN_pNorm = a_eps * tf.pow(dUNN_Norm, p_index) # * 行 1 列
if R['equa_name'] == 'Boltzmann3' or R['equa_name'] == 'Boltzmann4' or\
R['equa_name'] == 'Boltzmann5' or R['equa_name'] == 'Boltzmann6':
fxy = MS_BoltzmannEqs.get_foreside2Boltzmann2D(x=X_it, y=Y_it)
loss_it_variational = (1.0 / p_index) * (AdUNN_pNorm + Kappa*UNN*UNN) - \
tf.multiply(tf.reshape(fxy, shape=[-1, 1]), UNN)
else:
loss_it_variational = (1.0 / p_index) * (AdUNN_pNorm + Kappa * UNN * UNN) - \
tf.multiply(tf.reshape(f(X_it, Y_it), shape=[-1, 1]), UNN)
loss_it = tf.reduce_mean(loss_it_variational)
elif R['loss_type'] == 'lncosh_loss2Ritz':
dUNN = tf.gradients(UNN, XY_it)[0] # * 行 2 列
dUNN_Norm = tf.reshape(tf.sqrt(tf.reduce_sum(tf.square(dUNN), axis=-1)), shape=[-1, 1]) # 按行求和
if R['PDE_type'] == 'general_Laplace':
dUNN_2Norm = tf.square(dUNN_Norm)
loss_it_variational = (1.0 / 2) * dUNN_2Norm - \
tf.multiply(tf.reshape(f(X_it, Y_it), shape=[-1, 1]), UNN)
cosh_loss_it = tf.cosh(lambda2lncosh * loss_it_variational)
loss_lncosh_it = (1.0 / lambda2lncosh)*tf.log(cosh_loss_it)
elif R['PDE_type'] == 'pLaplace_explicit' or R['PDE_type'] == 'pLaplace_implicit':
a_eps = A_eps(X_it, Y_it) # * 行 1 列
AdUNN_pNorm = tf.multiply(a_eps, tf.pow(dUNN_Norm, p_index))
if R['equa_name'] == 'multi_scale2D_7':
fxy = MS_LaplaceEqs.get_force_side2MS_E7(x=X_it, y=Y_it)
loss_it_variational = (1.0 / p_index) * AdUNN_pNorm - \
tf.multiply(tf.reshape(fxy, shape=[-1, 1]), UNN)
else:
loss_it_variational = (1.0 / p_index) * AdUNN_pNorm - \
tf.multiply(tf.reshape(f(X_it, Y_it), shape=[-1, 1]), UNN)
cosh_loss_it = tf.cosh(lambda2lncosh * loss_it_variational)
loss_lncosh_it = (1.0 / lambda2lncosh)*tf.log(cosh_loss_it)
elif R['PDE_type'] == 'Possion_Boltzmann':
a_eps = A_eps(X_it, Y_it) # * 行 1 列
Kappa = kappa(X_it, Y_it) # * 行 1 列
AdUNN_pNorm = a_eps * tf.pow(dUNN_Norm, p_index) # * 行 1 列
if R['equa_name'] == 'Boltzmann3' or R['equa_name'] == 'Boltzmann4' or \
R['equa_name'] == 'Boltzmann5' or R['equa_name'] == 'Boltzmann6':
fxy = MS_BoltzmannEqs.get_foreside2Boltzmann2D(x=X_it, y=Y_it)
loss_it_variational = (1.0 / p_index) * (AdUNN_pNorm + Kappa * UNN * UNN) - \
tf.multiply(tf.reshape(fxy, shape=[-1, 1]), UNN)
else:
loss_it_variational = (1.0 / p_index) * (AdUNN_pNorm + Kappa * UNN * UNN) - \
tf.multiply(tf.reshape(f(X_it, Y_it), shape=[-1, 1]), UNN)
cosh_loss_it = tf.cosh(lambda2lncosh * loss_it_variational)
loss_lncosh_it = (1.0 / lambda2lncosh)*tf.log(cosh_loss_it)
loss_it = tf.reduce_mean(loss_lncosh_it)
elif R['loss_type'] == 'L2_loss':
dUNN = tf.gradients(UNN, XY_it)[0] # * 行 2 列
if R['PDE_type'] == 'general_Laplace':
dUNNx = tf.gather(dUNN, [0], axis=-1)
dUNNy = tf.gather(dUNN, [1], axis=-1)
dUNNxxy = tf.gradients(dUNNx, XY_it)[0]
dUNNyxy = tf.gradients(dUNNy, XY_it)[0]
dUNNxx = tf.gather(dUNNxxy, [0], axis=-1)
dUNNyy = tf.gather(dUNNyxy, [1], axis=-1)
# -Laplace U=f --> -Laplace U - f --> -(Laplace U + f)
loss_it_L2 = tf.add(dUNNxx, dUNNyy) + tf.reshape(f(X_it, Y_it), shape=[-1, 1])
square_loss_it = tf.square(loss_it_L2)
elif R['PDE_type'] == 'Convection_diffusion':
a_eps = A_eps(X_it, Y_it) # * 行 1 列
bx = Bx(X_it, Y_it)
by = By(X_it, Y_it)
dUNNx = tf.gather(dUNN, [0], axis=-1)
dUNNy = tf.gather(dUNN, [1], axis=-1)
dUNNxxy = tf.gradients(dUNNx, XY_it)[0]
dUNNyxy = tf.gradients(dUNNy, XY_it)[0]
dUNNxx = tf.gather(dUNNxxy, [0], axis=-1)
dUNNyy = tf.gather(dUNNyxy, [1], axis=-1)
ddUNN = tf.add(dUNNxx, dUNNyy)
bdUNN = bx * dUNNx + by * dUNNy
loss_it_L2 = -a_eps*ddUNN + bdUNN - f(X_it, Y_it)
square_loss_it = tf.square(loss_it_L2)
elif R['PDE_type'] == 'pLaplace_explicit' or R['PDE_type'] == 'pLaplace_implicit':
a_eps = A_eps(X_it, Y_it)
dUNNxy_norm = tf.reshape(tf.sqrt(tf.reduce_sum(tf.square(dUNN), axis=-1)), shape=[-1, 1]) # 按行求和
dUNNx = tf.gather(dUNN, [0], axis=-1)
dUNNy = tf.gather(dUNN, [1], axis=-1)
if p_index == 2:
dUxdUnorm = dUNNx
dUydUnorm = dUNNy
else:
dUxdUnorm = tf.multiply(tf.pow(dUNNxy_norm, p_index - 2), dUNNx)
dUydUnorm = tf.multiply(tf.pow(dUNNxy_norm, p_index - 2), dUNNy)
AdUxdUnorm = tf.multiply(a_eps, dUxdUnorm)
AdUydUnorm = tf.multiply(a_eps, dUydUnorm)
dAdUxdUnorm_xy = tf.gradients(AdUxdUnorm, XY_it)[0]
dAdUydUnorm_xy = tf.gradients(AdUydUnorm, XY_it)[0]
dAdUxdUnorm_x = tf.gather(dAdUxdUnorm_xy, [0], axis=-1)
dAdUydUnorm_y = tf.gather(dAdUydUnorm_xy, [1], axis=-1)
div_AdUdUnorm = tf.add(dAdUxdUnorm_x, dAdUydUnorm_y)
loss_it_L2 = -div_AdUdUnorm - f(X_it, Y_it)
square_loss_it = tf.square(loss_it_L2)
elif R['PDE_type'] == 'Possion_Boltzmann':
a_eps = A_eps(X_it, Y_it)
Kappa = kappa(X_it, Y_it) # * 行 1 列
dUNNxy_norm = tf.reshape(tf.sqrt(tf.reduce_sum(tf.square(dUNN), axis=-1)), shape=[-1, 1]) # 按行求和
dUNNx = tf.gather(dUNN, [0], axis=-1)
dUNNy = tf.gather(dUNN, [1], axis=-1)
if p_index == 2:
dUxdUnorm = dUNNx
dUydUnorm = dUNNy
else:
dUxdUnorm = tf.multiply(tf.pow(dUNNxy_norm, p_index - 2), dUNNx)
dUydUnorm = tf.multiply(tf.pow(dUNNxy_norm, p_index - 2), dUNNy)
AdUxdUnorm = tf.multiply(a_eps, dUxdUnorm)
AdUydUnorm = tf.multiply(a_eps, dUydUnorm)
dAdUxdUnorm_xy = tf.gradients(AdUxdUnorm, XY_it)[0]
dAdUydUnorm_xy = tf.gradients(AdUydUnorm, XY_it)[0]
dAdUxdUnorm_x = tf.gather(dAdUxdUnorm_xy, [0], axis=-1)
dAdUydUnorm_y = tf.gather(dAdUydUnorm_xy, [1], axis=-1)
div_AdUdUnorm = tf.add(dAdUxdUnorm_x, dAdUydUnorm_y)
KU = tf.multiply(Kappa, UNN)
loss_it_L2 = -div_AdUdUnorm + KU - f(X_it, Y_it)
square_loss_it = tf.square(loss_it_L2)
# loss_it = tf.reduce_mean(square_loss_it) * (region_rt - region_lb) * (region_rt - region_lb)
loss_it = tf.reduce_mean(square_loss_it)
U_left = u_left(tf.reshape(XY_left[:, 0], shape=[-1, 1]), tf.reshape(XY_left[:, 1], shape=[-1, 1]))
U_right = u_right(tf.reshape(XY_right[:, 0], shape=[-1, 1]), tf.reshape(XY_right[:, 1], shape=[-1, 1]))
U_bottom = u_bottom(tf.reshape(XY_bottom[:, 0], shape=[-1, 1]), tf.reshape(XY_bottom[:, 1], shape=[-1, 1]))
U_top = u_top(tf.reshape(XY_top[:, 0], shape=[-1, 1]), tf.reshape(XY_top[:, 1], shape=[-1, 1]))
if R['loss_type'] == 'lncosh_loss2Ritz':
cosh_bd = tf.cosh(lambda2lncosh*(UNN_left-U_left))+tf.cosh(lambda2lncosh*(UNN_right-U_right)) + \
tf.cosh(lambda2lncosh * (UNN_bottom - U_bottom)) + tf.cosh(lambda2lncosh * (UNN_top - U_top))
loss_cosh_bd = (1.0 / lambda2lncosh) * tf.log(cosh_bd)
loss_bd = tf.reduce_mean(loss_cosh_bd)
else:
loss_bd_square = tf.square(UNN_left - U_left) + tf.square(UNN_right - U_right) + \
tf.square(UNN_bottom - U_bottom) + tf.square(UNN_top - U_top)
loss_bd = tf.reduce_mean(loss_bd_square)
if R['regular_wb_model'] == 'L1':
regularSum2WB = DNN_base.regular_weights_biases_L1(W2NN, B2NN) # 正则化权重和偏置 L1正则化
elif R['regular_wb_model'] == 'L2':
regularSum2WB = DNN_base.regular_weights_biases_L2(W2NN, B2NN) # 正则化权重和偏置 L2正则化
else:
regularSum2WB = tf.constant(0.0) # 无正则化权重参数
PWB = penalty2WB * regularSum2WB
loss = loss_it + boundary_penalty * loss_bd + PWB # 要优化的loss function
my_optimizer = tf.compat.v1.train.AdamOptimizer(in_learning_rate)
if R['train_model'] == 'group3_training':
train_op1 = my_optimizer.minimize(loss_it, global_step=global_steps)
train_op2 = my_optimizer.minimize(loss_bd, global_step=global_steps)
train_op3 = my_optimizer.minimize(loss, global_step=global_steps)
train_my_loss = tf.group(train_op1, train_op2, train_op3)
elif R['train_model'] == 'group2_training':
train_op2bd = my_optimizer.minimize(loss_bd, global_step=global_steps)
train_op2union = my_optimizer.minimize(loss, global_step=global_steps)
train_my_loss = tf.group(train_op2bd, train_op2union)
elif R['train_model'] == 'union_training':
train_my_loss = my_optimizer.minimize(loss, global_step=global_steps)
# 训练上的真解值和训练结果的误差
if R['PDE_type'] == 'general_Laplace' or R['PDE_type'] == 'pLaplace_explicit' \
or R['PDE_type'] == 'Possion_Boltzmann' or R['PDE_type'] == 'Convection_diffusion':
U_true = u_true(X_it, Y_it)
train_mse = tf.reduce_mean(tf.square(U_true - UNN))
train_rel = train_mse / tf.reduce_mean(tf.square(U_true))
else:
train_mse = tf.constant(0.0)
train_rel = tf.constant(0.0)
t0 = time.time()
loss_it_all, loss_bd_all, loss_all, train_mse_all, train_rel_all = [], [], [], [], [] # 空列表, 使用 append() 添加元素
test_mse_all, test_rel_all = [], []
test_epoch = []
if R['testData_model'] == 'random_generate':
# 生成测试数据，用于测试训练后的网络
test_bach_size = 1600
size2test = 40
# test_bach_size = 4900
# size2test = 70
# test_bach_size = 10000
# size2test = 100
# test_bach_size = 40000
# size2test = 200
test_xy_bach = DNN_data.rand_it(test_bach_size, input_dim, region_lb, region_rt)
saveData.save_testData_or_solus2mat(test_xy_bach, dataName='testXY', outPath=R['FolderName'])
else:
if R['PDE_type'] == 'pLaplace_implicit' or R['PDE_type'] == 'pLaplace_explicit':
test_xy_bach = Load_data2Mat.get_data2pLaplace(equation_name=R['equa_name'], mesh_number=mesh_number)
size2batch = np.shape(test_xy_bach)[0]
size2test = int(np.sqrt(size2batch))
saveData.save_meshData2mat(test_xy_bach, dataName='meshXY', mesh_number=mesh_number, outPath=R['FolderName'])
elif R['PDE_type'] == 'Possion_Boltzmann':
if region_lb == (-1.0) and region_rt == 1.0:
name2data_file = '11'
else:
name2data_file = '01'
test_xy_bach = Load_data2Mat.get_meshData2Boltzmann(domain_lr=name2data_file, mesh_number=mesh_number)
size2batch = np.shape(test_xy_bach)[0]
size2test = int(np.sqrt(size2batch))
saveData.save_meshData2mat(test_xy_bach, dataName='meshXY', mesh_number=mesh_number,
outPath=R['FolderName'])
elif R['PDE_type'] == 'Convection_diffusion':
if region_lb == (-1.0) and region_rt == 1.0:
name2data_file = '11'
else:
name2data_file = '01'
test_xy_bach = Load_data2Mat.get_meshData2Boltzmann(domain_lr=name2data_file, mesh_number=mesh_number)
size2batch = np.shape(test_xy_bach)[0]
size2test = int(np.sqrt(size2batch))
saveData.save_meshData2mat(test_xy_bach, dataName='meshXY', mesh_number=mesh_number,
outPath=R['FolderName'])
else:
test_xy_bach = Load_data2Mat.get_randomData2mat(dim=input_dim, data_path='dataMat_highDim')
size2batch = np.shape(test_xy_bach)[0]
size2test = int(np.sqrt(size2batch))
# ConfigProto 加上allow_soft_placement=True就可以使用 gpu 了
config = tf.compat.v1.ConfigProto(allow_soft_placement=True) # 创建sess的时候对sess进行参数配置
config.gpu_options.allow_growth = True # True是让TensorFlow在运行过程中动态申请显存，避免过多的显存占用。
config.allow_soft_placement = True # 当指定的设备不存在时，允许选择一个存在的设备运行。比如gpu不存在，自动降到cpu上运行
with tf.compat.v1.Session(config=config) as sess:
sess.run(tf.compat.v1.global_variables_initializer())
tmp_lr = learning_rate
for i_epoch in range(R['max_epoch'] + 1):
xy_it_batch = DNN_data.rand_it(batchsize_it, input_dim, region_a=region_lb, region_b=region_rt)
xl_bd_batch, xr_bd_batch, yb_bd_batch, yt_bd_batch = DNN_data.rand_bd_2D(
batchsize_bd, input_dim, region_a=region_lb, region_b=region_rt)
tmp_lr = tmp_lr * (1 - lr_decay)
if R['activate_penalty2bd_increase'] == 1:
if i_epoch < int(R['max_epoch'] / 10):
temp_penalty_bd = bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 5):
temp_penalty_bd = 10 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 4):
temp_penalty_bd = 50 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 2):
temp_penalty_bd = 100 * bd_penalty_init
elif i_epoch < int(3 * R['max_epoch'] / 4):
temp_penalty_bd = 200 * bd_penalty_init
else:
temp_penalty_bd = 500 * bd_penalty_init
else:
temp_penalty_bd = bd_penalty_init
_, loss_it_tmp, loss_bd_tmp, loss_tmp, train_mse_tmp, train_rel_tmp, pwb = sess.run(
[train_my_loss, loss_it, loss_bd, loss, train_mse, train_rel, PWB],
feed_dict={XY_it: xy_it_batch, XY_left: xl_bd_batch, XY_right: xr_bd_batch,
XY_bottom: yb_bd_batch, XY_top: yt_bd_batch, in_learning_rate: tmp_lr,
boundary_penalty: temp_penalty_bd})
loss_it_all.append(loss_it_tmp)
loss_bd_all.append(loss_bd_tmp)
loss_all.append(loss_tmp)
train_mse_all.append(train_mse_tmp)
train_rel_all.append(train_rel_tmp)
if i_epoch % 1000 == 0:
run_times = time.time() - t0
DNN_Log_Print.print_and_log_train_one_epoch(
i_epoch, run_times, tmp_lr, temp_penalty_bd, pwb, loss_it_tmp, loss_bd_tmp, loss_tmp, train_mse_tmp,
train_rel_tmp, log_out=log_fileout)
# --------------------------- test network ----------------------------------------------
test_epoch.append(i_epoch / 1000)
if R['PDE_type'] == 'general_Laplace' or R['PDE_type'] == 'pLaplace_explicit' or \
R['PDE_type'] == 'Possion_Boltzmann' or R['PDE_type'] == 'Convection_diffusion':
u_true2test, unn2test = sess.run([U_true, UNN], feed_dict={XY_it: test_xy_bach})
else:
u_true2test = u_true
unn2test = sess.run(UNN, feed_dict={XY_it: test_xy_bach})
point_square_error = np.square(u_true2test - unn2test)
mse2test = np.mean(point_square_error)
test_mse_all.append(mse2test)
res2test = mse2test / np.mean(np.square(u_true2test))
test_rel_all.append(res2test)
DNN_Log_Print.print_and_log_test_one_epoch(mse2test, res2test, log_out=log_fileout)
# ------------------- save the testing results into mat file and plot them -------------------------
saveData.save_trainLoss2mat_1actFunc(loss_it_all, loss_bd_all, loss_all, actName=act_func,
outPath=R['FolderName'])
saveData.save_train_MSE_REL2mat(train_mse_all, train_rel_all, actName=act_func, outPath=R['FolderName'])
plotData.plotTrain_loss_1act_func(loss_it_all, lossType='loss_it', seedNo=R['seed'], outPath=R['FolderName'])
plotData.plotTrain_loss_1act_func(loss_bd_all, lossType='loss_bd', seedNo=R['seed'], outPath=R['FolderName'],
yaxis_scale=True)
plotData.plotTrain_loss_1act_func(loss_all, lossType='loss', seedNo=R['seed'], outPath=R['FolderName'])
saveData.save_train_MSE_REL2mat(train_mse_all, train_rel_all, actName=act_func, outPath=R['FolderName'])
plotData.plotTrain_MSE_REL_1act_func(train_mse_all, train_rel_all, actName=act_func, seedNo=R['seed'],
outPath=R['FolderName'], yaxis_scale=True)
# ---------------------- save testing results to mat files, then plot them --------------------------------
saveData.save_2testSolus2mat(u_true2test, unn2test, actName='utrue', actName1=act_func,
outPath=R['FolderName'])
plotData.plot_Hot_solution2test(u_true2test, size_vec2mat=size2test, actName='Utrue', seedNo=R['seed'],
outPath=R['FolderName'])
plotData.plot_Hot_solution2test(unn2test, size_vec2mat=size2test, actName=act_func, seedNo=R['seed'],
outPath=R['FolderName'])
saveData.save_testMSE_REL2mat(test_mse_all, test_rel_all, actName=act_func, outPath=R['FolderName'])
plotData.plotTest_MSE_REL(test_mse_all, test_rel_all, test_epoch, actName=act_func,
seedNo=R['seed'], outPath=R['FolderName'], yaxis_scale=True)
saveData.save_test_point_wise_err2mat(point_square_error, actName=act_func, outPath=R['FolderName'])
plotData.plot_Hot_point_wise_err(point_square_error, size_vec2mat=size2test, actName=act_func,
seedNo=R['seed'], outPath=R['FolderName'])
def solve_Multiscale_PDE(R):
log_out_path = R['FolderName'] # 将路径从字典 R 中提取出来
if not os.path.exists(log_out_path): # 判断路径是否已经存在
os.mkdir(log_out_path) # 无 log_out_path 路径，创建一个 log_out_path 路径
logfile_name = '%s%s.txt' % ('log2', R['name2act_hidden'])
log_fileout = open(os.path.join(log_out_path, logfile_name),
'w') # 在这个路径下创建并打开一个可写的 log_train.txt文件
DNN_Log_Print.dictionary_out2file(R, log_fileout)
# 一般 laplace 问题需要的设置
batchsize_it = R['batch_size2interior']
batchsize_bd = R['batch_size2boundary']
bd_penalty_init = R[
'init_boundary_penalty'] # Regularization parameter for boundary conditions
penalty2WB = R[
'penalty2weight_biases'] # Regularization parameter for weights and biases
lr_decay = R['learning_rate_decay']
learning_rate = R['learning_rate']
hidden_layers = R['hidden_layers']
input_dim = R['input_dim']
out_dim = R['output_dim']
act_func = R['name2act_hidden']
# p laplace 问题需要的额外设置, 先预设一下
p_index = R['order2pLaplace_operator']
mesh_number = 2
region_lb = 0.0
region_rt = 1.0
if R['PDE_type'] == 'general_Laplace':
# -laplace u = f
region_lb = 0.0
region_rt = 1.0
f, u_true, u00, u01, u10, u11, u20, u21, u30, u31, u40, u41 = General_Laplace.get_infos2Laplace_5D(
input_dim=input_dim,
out_dim=out_dim,
intervalL=region_lb,
intervalR=region_rt,
equa_name=R['equa_name'])
elif R['PDE_type'] == 'pLaplace':
region_lb = 0.0
region_rt = 1.0
u_true, f, A_eps, u00, u01, u10, u11, u20, u21, u30, u31, u40, u41 = MS_LaplaceEqs.get_infos2pLaplace_5D(
input_dim=input_dim,
out_dim=out_dim,
intervalL=0.0,
intervalR=1.0,
equa_name=R['equa_name'])
elif R['PDE_type'] == 'Possion_Boltzmann':
region_lb = 0.0
region_rt = 1.0
u_true, f, A_eps, kappa, u00, u01, u10, u11, u20, u21, u30, u31, u40, u41 = MS_BoltzmannEqs.get_infos2Boltzmann_5D(
input_dim=input_dim,
out_dim=out_dim,
intervalL=0.0,
intervalR=1.0,
equa_name=R['equa_name'])
flag = 'WB2NN'
if R['model2NN'] == 'DNN_FourierBase':
W2NN, B2NN = DNN_base.Xavier_init_NN_Fourier(input_dim, out_dim,
hidden_layers, flag)
else:
W2NN, B2NN = DNN_base.Xavier_init_NN(input_dim, out_dim, hidden_layers,
flag)
global_steps = tf.compat.v1.Variable(0, trainable=False)
with tf.device('/gpu:%s' % (R['gpuNo'])):
with tf.compat.v1.variable_scope('vscope',
reuse=tf.compat.v1.AUTO_REUSE):
XYZST_it = tf.compat.v1.placeholder(tf.float32,
name='XYZST_it',
shape=[None, input_dim])
XYZST00 = tf.compat.v1.placeholder(tf.float32,
name='XYZST00',
shape=[None, input_dim])
XYZST01 = tf.compat.v1.placeholder(tf.float32,
name='XYZST01',
shape=[None, input_dim])
XYZST10 = tf.compat.v1.placeholder(tf.float32,
name='XYZST10',
shape=[None, input_dim])
XYZST11 = tf.compat.v1.placeholder(tf.float32,
name='XYZST11',
shape=[None, input_dim])
XYZST20 = tf.compat.v1.placeholder(tf.float32,
name='XYZST20',
shape=[None, input_dim])
XYZST21 = tf.compat.v1.placeholder(tf.float32,
name='XYZST21',
shape=[None, input_dim])
XYZST30 = tf.compat.v1.placeholder(tf.float32,
name='XYZST30',
shape=[None, input_dim])
XYZST31 = tf.compat.v1.placeholder(tf.float32,
name='XYZST31',
shape=[None, input_dim])
XYZST40 = tf.compat.v1.placeholder(tf.float32,
name='XYZST40',
shape=[None, input_dim])
XYZST41 = tf.compat.v1.placeholder(tf.float32,
name='XYZST41',
shape=[None, input_dim])
boundary_penalty = tf.compat.v1.placeholder_with_default(
input=1e3, shape=[], name='bd_p')
in_learning_rate = tf.compat.v1.placeholder_with_default(
input=1e-5, shape=[], name='lr')
# 供选择的网络模式
if R['model2NN'] == 'DNN':
UNN = DNN_base.DNN(XYZST_it,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U00_NN = DNN_base.DNN(XYZST00,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U01_NN = DNN_base.DNN(XYZST01,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U10_NN = DNN_base.DNN(XYZST10,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U11_NN = DNN_base.DNN(XYZST11,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U20_NN = DNN_base.DNN(XYZST20,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U21_NN = DNN_base.DNN(XYZST21,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U30_NN = DNN_base.DNN(XYZST30,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U31_NN = DNN_base.DNN(XYZST31,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U40_NN = DNN_base.DNN(XYZST40,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U41_NN = DNN_base.DNN(XYZST41,
W2NN,
B2NN,
hidden_layers,
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
elif R['model2NN'] == 'DNN_scale':
UNN = DNN_base.DNN_scale(XYZST_it,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U00_NN = DNN_base.DNN_scale(XYZST00,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U01_NN = DNN_base.DNN_scale(XYZST01,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U10_NN = DNN_base.DNN_scale(XYZST10,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U11_NN = DNN_base.DNN_scale(XYZST11,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U20_NN = DNN_base.DNN_scale(XYZST20,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U21_NN = DNN_base.DNN_scale(XYZST21,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U30_NN = DNN_base.DNN_scale(XYZST30,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U31_NN = DNN_base.DNN_scale(XYZST31,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U40_NN = DNN_base.DNN_scale(XYZST40,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U41_NN = DNN_base.DNN_scale(XYZST41,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
elif R['model2NN'] == 'DNN_adapt_scale':
UNN = DNN_base.DNN_adapt_scale(
XYZST_it,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U00_NN = DNN_base.DNN_adapt_scale(
XYZST00,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U01_NN = DNN_base.DNN_adapt_scale(
XYZST01,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U10_NN = DNN_base.DNN_adapt_scale(
XYZST10,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U11_NN = DNN_base.DNN_adapt_scale(
XYZST11,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U20_NN = DNN_base.DNN_adapt_scale(
XYZST20,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U21_NN = DNN_base.DNN_adapt_scale(
XYZST21,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U30_NN = DNN_base.DNN_adapt_scale(
XYZST30,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U31_NN = DNN_base.DNN_adapt_scale(
XYZST31,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U40_NN = DNN_base.DNN_adapt_scale(
XYZST40,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
U41_NN = DNN_base.DNN_adapt_scale(
XYZST41,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'])
elif R['model2NN'] == 'DNN_FourierBase':
UNN = DNN_base.DNN_FourierBase(
XYZST_it,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U00_NN = DNN_base.DNN_FourierBase(
XYZST00,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U01_NN = DNN_base.DNN_FourierBase(
XYZST01,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U10_NN = DNN_base.DNN_FourierBase(
XYZST10,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U11_NN = DNN_base.DNN_FourierBase(
XYZST11,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U20_NN = DNN_base.DNN_FourierBase(
XYZST20,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U21_NN = DNN_base.DNN_FourierBase(
XYZST21,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U30_NN = DNN_base.DNN_FourierBase(
XYZST30,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U31_NN = DNN_base.DNN_FourierBase(
XYZST31,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U40_NN = DNN_base.DNN_FourierBase(
XYZST40,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
U41_NN = DNN_base.DNN_FourierBase(
XYZST41,
W2NN,
B2NN,
hidden_layers,
R['freq'],
activate_name=R['name2act_hidden'],
sFourier=R['sfourier'])
X_it = tf.reshape(XYZST_it[:, 0], shape=[-1, 1])
Y_it = tf.reshape(XYZST_it[:, 1], shape=[-1, 1])
Z_it = tf.reshape(XYZST_it[:, 2], shape=[-1, 1])
S_it = tf.reshape(XYZST_it[:, 3], shape=[-1, 1])
T_it = tf.reshape(XYZST_it[:, 4], shape=[-1, 1])
dUNN = tf.gradients(UNN, XYZST_it)[0] # * 行 2 列
# 变分形式的loss of interior，训练得到的 UNN 是 * 行 1 列, 因为 一个点对(x,y) 得到一个 u 值
if R['loss_type'] == 'variational_loss':
dUNN_Norm = tf.reshape(tf.sqrt(
tf.reduce_sum(tf.square(dUNN), axis=-1)),
shape=[-1, 1]) # 按行求和
if R['PDE_type'] == 'general_Laplace':
dUNN_2Norm = tf.square(dUNN_Norm)
loss_it_variational = (1.0 / 2) * dUNN_2Norm - tf.multiply(
f(X_it, Y_it, Z_it, S_it, T_it), UNN)
elif R['PDE_type'] == 'pLaplace':
a_eps = A_eps(X_it, Y_it, Z_it, S_it, T_it) # * 行 1 列
AdUNN_pNorm = a_eps * tf.pow(dUNN_Norm, p_index)
if R['equa_name'] == 'multi_scale5D_4' or R['equa_name'] == 'multi_scale5D_5' or \
R['equa_name'] == 'multi_scale5D_6' or R['equa_name'] == 'multi_scale5D_7':
fxyzst = MS_LaplaceEqs.get_forceSide2pLaplace5D(
x=X_it,
y=Y_it,
z=Z_it,
s=S_it,
t=T_it,
equa_name=R['equa_name'])
loss_it_variational = (
1.0 / p_index) * AdUNN_pNorm - tf.multiply(
tf.reshape(fxyzst, shape=[-1, 1]), UNN)
else:
loss_it_variational = (
1.0 / p_index) * AdUNN_pNorm - tf.multiply(
f(X_it, Y_it, Z_it, S_it, T_it), UNN)
elif R['PDE_type'] == 'Possion_Boltzmann':
a_eps = A_eps(X_it, Y_it, Z_it, S_it, T_it) # * 行 1 列
AdUNN_pNorm = a_eps * tf.pow(dUNN_Norm, p_index)
Kappa = np.pi * np.pi
# Kappa = kappa(X_it, Y_it, Z_it, S_it, T_it)
if R['equa_name'] == 'multi_scale5D_4' or R['equa_name'] == 'multi_scale5D_5' or \
R['equa_name'] == 'multi_scale5D_6' or R['equa_name'] == 'multi_scale5D_7':
fxyzst = MS_BoltzmannEqs.get_forceSide2Boltzmann_5D(
x=X_it,
y=Y_it,
z=Z_it,
s=S_it,
t=T_it,
equa_name=R['equa_name'])
loss_it_variational = (1.0 / p_index) * (
AdUNN_pNorm + Kappa * UNN * UNN) - tf.multiply(
fxyzst, UNN)
else:
loss_it_variational = (1.0 / p_index) * (AdUNN_pNorm + Kappa*UNN*UNN) - \
tf.multiply(f(X_it, Y_it, Z_it, S_it, T_it), UNN)
loss_it = tf.reduce_mean(loss_it_variational)
U_00 = tf.constant(0.0)
U_01 = tf.constant(0.0)
U_10 = tf.constant(0.0)
U_11 = tf.constant(0.0)
U_20 = tf.constant(0.0)
U_21 = tf.constant(0.0)
U_30 = tf.constant(0.0)
U_31 = tf.constant(0.0)
U_40 = tf.constant(0.0)
U_41 = tf.constant(0.0)
loss_bd_square2NN = tf.square(U00_NN - U_00) + tf.square(U01_NN - U_01) + tf.square(U10_NN - U_10) + \
tf.square(U11_NN - U_11) + tf.square(U20_NN - U_20) + tf.square(U21_NN - U_21) + \
tf.square(U30_NN - U_30) + tf.square(U31_NN - U_31) + tf.square(U40_NN - U_40) + \
tf.square(U41_NN - U_41)
loss_bd = tf.reduce_mean(loss_bd_square2NN)
if R['regular_wb_model'] == 'L1':
regularSum2WB = DNN_base.regular_weights_biases_L1(
W2NN, B2NN) # 正则化权重和偏置 L1正则化
elif R['regular_wb_model'] == 'L2':
regularSum2WB = DNN_base.regular_weights_biases_L2(
W2NN, B2NN) # 正则化权重和偏置 L2正则化
else:
regularSum2WB = tf.constant(0.0) # 无正则化权重参数
PWB = penalty2WB * regularSum2WB
loss = loss_it + boundary_penalty * loss_bd + PWB # 要优化的loss function
my_optimizer = tf.train.AdamOptimizer(in_learning_rate)
if R['train_model'] == 'group3_training':
train_op1 = my_optimizer.minimize(loss_it,
global_step=global_steps)
train_op2 = my_optimizer.minimize(loss_bd,
global_step=global_steps)
train_op3 = my_optimizer.minimize(loss,
global_step=global_steps)
train_my_loss = tf.group(train_op1, train_op2, train_op3)
elif R['train_model'] == 'group2_training':
train_op2bd = my_optimizer.minimize(loss_bd,
global_step=global_steps)
train_op2union = my_optimizer.minimize(
loss, global_step=global_steps)
train_my_loss = tf.group(train_op2union, train_op2bd)
elif R['train_model'] == 'union_training':
train_my_loss = my_optimizer.minimize(loss,
global_step=global_steps)
if R['PDE_type'] == 'general_Laplace' or R[
'PDE_type'] == 'pLaplace' or R[
'PDE_type'] == 'Possion_Boltzmann':
# 训练上的真解值和训练结果的误差
U_true = u_true(X_it, Y_it, Z_it, S_it, T_it)
train_mse = tf.reduce_mean(tf.square(U_true - UNN))
train_rel = train_mse / tf.reduce_mean(tf.square(U_true))
else:
train_mse = tf.constant(0.0)
train_rel = tf.constant(0.0)
t0 = time.time()
loss_it_all, loss_bd_all, loss_all, train_mse_all, train_rel_all = [], [], [], [], [] # 空列表, 使用 append() 添加元素
test_mse_all, test_rel_all = [], []
test_epoch = []
# 画网格解图
if R['testData_model'] == 'random_generate':
# 生成测试数据，用于测试训练后的网络
# test_bach_size = 400
# size2test = 20
# test_bach_size = 900
# size2test = 30
test_bach_size = 1600
size2test = 40
# test_bach_size = 4900
# size2test = 70
# test_bach_size = 10000
# size2test = 100
test_xyzst_bach = DNN_data.rand_it(test_bach_size, input_dim,
region_lb, region_rt)
saveData.save_testData_or_solus2mat(test_xyzst_bach,
dataName='testXYZST',
outPath=R['FolderName'])
elif R['testData_model'] == 'loadData':
test_bach_size = 1600
size2test = 40
mat_data_path = 'dataMat_highDim'
test_xyzst_bach = Load_data2Mat.get_randomData2mat(
dim=input_dim, data_path=mat_data_path)
saveData.save_testData_or_solus2mat(test_xyzst_bach,
dataName='testXYZST',
outPath=R['FolderName'])
# ConfigProto 加上allow_soft_placement=True就可以使用 gpu 了
config = tf.ConfigProto(allow_soft_placement=True) # 创建sess的时候对sess进行参数配置
config.gpu_options.allow_growth = True # True是让TensorFlow在运行过程中动态申请显存，避免过多的显存占用。
config.allow_soft_placement = True # 当指定的设备不存在时，允许选择一个存在的设备运行。比如gpu不存在，自动降到cpu上运行
with tf.Session(config=config) as sess:
sess.run(tf.global_variables_initializer())
tmp_lr = learning_rate
for i_epoch in range(R['max_epoch'] + 1):
xyzst_it_batch = DNN_data.rand_it(batchsize_it,
input_dim,
region_a=region_lb,
region_b=region_rt)
xyzst00_batch, xyzst01_batch, xyzst10_batch, xyzst11_batch, xyzst20_batch, xyzst21_batch, xyzst30_batch, \
xyzst31_batch, xyzst40_batch, xyzst41_batch = DNN_data.rand_bd_5D(batchsize_bd, input_dim,
region_a=region_lb, region_b=region_rt)
tmp_lr = tmp_lr * (1 - lr_decay)
if R['activate_penalty2bd_increase'] == 1:
if i_epoch < int(R['max_epoch'] / 10):
temp_penalty_bd = bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 5):
temp_penalty_bd = 10 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 4):
temp_penalty_bd = 50 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 2):
temp_penalty_bd = 100 * bd_penalty_init
elif i_epoch < int(3 * R['max_epoch'] / 4):
temp_penalty_bd = 200 * bd_penalty_init
else:
temp_penalty_bd = 500 * bd_penalty_init
elif R['activate_penalty2bd_increase'] == 2:
if i_epoch < int(R['max_epoch'] / 10):
temp_penalty_bd = 5 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 5):
temp_penalty_bd = 1 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 4):
temp_penalty_bd = 0.5 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 2):
temp_penalty_bd = 0.1 * bd_penalty_init
elif i_epoch < int(3 * R['max_epoch'] / 4):
temp_penalty_bd = 0.05 * bd_penalty_init
else:
temp_penalty_bd = 0.02 * bd_penalty_init
else:
temp_penalty_bd = bd_penalty_init
_, loss_it_tmp, loss_bd_tmp, loss_tmp, train_mse_tmp, train_rel_tmp, pwb = sess.run(
[
train_my_loss, loss_it, loss_bd, loss, train_mse,
train_rel, PWB
],
feed_dict={
XYZST_it: xyzst_it_batch,
XYZST00: xyzst00_batch,
XYZST01: xyzst01_batch,
XYZST10: xyzst10_batch,
XYZST11: xyzst11_batch,
XYZST20: xyzst20_batch,
XYZST21: xyzst21_batch,
XYZST30: xyzst30_batch,
XYZST31: xyzst31_batch,
XYZST40: xyzst40_batch,
XYZST41: xyzst41_batch,
in_learning_rate: tmp_lr,
boundary_penalty: temp_penalty_bd
})
loss_it_all.append(loss_it_tmp)
loss_bd_all.append(loss_bd_tmp)
loss_all.append(loss_tmp)
train_mse_all.append(train_mse_tmp)
train_rel_all.append(train_rel_tmp)
if i_epoch % 1000 == 0:
run_times = time.time() - t0
DNN_Log_Print.print_and_log_train_one_epoch(
i_epoch,
run_times,
tmp_lr,
temp_penalty_bd,
pwb,
loss_it_tmp,
loss_bd_tmp,
loss_tmp,
train_mse_tmp,
train_rel_tmp,
log_out=log_fileout)
# --------------------------- test network ----------------------------------------------
test_epoch.append(i_epoch / 1000)
train_option = False
if R['PDE_type'] == 'general_laplace' or R[
'PDE_type'] == 'pLaplace' or R[
'PDE_type'] == 'Possion_Boltzmann':
u_true2test, u_nn2test = sess.run(
[U_true, UNN], feed_dict={XYZST_it: test_xyzst_bach})
else:
u_true2test = u_true
u_nn2test = sess.run(UNN,
feed_dict={XYZST_it: test_xyzst_bach})
point_square_error = np.square(u_true2test - u_nn2test)
mse2test = np.mean(point_square_error)
test_mse_all.append(mse2test)
res2test = mse2test / np.mean(np.square(u_true2test))
test_rel_all.append(res2test)
DNN_Log_Print.print_and_log_test_one_epoch(mse2test,
res2test,
log_out=log_fileout)
# ------------------- save the testing results into mat file and plot them -------------------------
saveData.save_trainLoss2mat_1actFunc(loss_it_all,
loss_bd_all,
loss_all,
actName=act_func,
outPath=R['FolderName'])
saveData.save_train_MSE_REL2mat(train_mse_all,
train_rel_all,
actName=act_func,
outPath=R['FolderName'])
plotData.plotTrain_loss_1act_func(loss_it_all,
lossType='loss_it',
seedNo=R['seed'],
outPath=R['FolderName'])
plotData.plotTrain_loss_1act_func(loss_bd_all,
lossType='loss_bd',
seedNo=R['seed'],
outPath=R['FolderName'],
yaxis_scale=True)
plotData.plotTrain_loss_1act_func(loss_all,
lossType='loss',
seedNo=R['seed'],
outPath=R['FolderName'])
saveData.save_train_MSE_REL2mat(train_mse_all,
train_rel_all,
actName=act_func,
outPath=R['FolderName'])
plotData.plotTrain_MSE_REL_1act_func(train_mse_all,
train_rel_all,
actName=act_func,
seedNo=R['seed'],
outPath=R['FolderName'],
yaxis_scale=True)
# ---------------------- save testing results to mat files, then plot them --------------------------------
saveData.save_2testSolus2mat(u_true2test,
u_nn2test,
actName='utrue',
actName1=act_func,
outPath=R['FolderName'])
# 绘制解的热力图(真解和DNN解)
plotData.plot_Hot_solution2test(u_true2test,
size_vec2mat=size2test,
actName='Utrue',
seedNo=R['seed'],
outPath=R['FolderName'])
plotData.plot_Hot_solution2test(u_nn2test,
size_vec2mat=size2test,
actName=act_func,
seedNo=R['seed'],
outPath=R['FolderName'])
saveData.save_testMSE_REL2mat(test_mse_all,
test_rel_all,
actName=act_func,
outPath=R['FolderName'])
plotData.plotTest_MSE_REL(test_mse_all,
test_rel_all,
test_epoch,
actName=act_func,
seedNo=R['seed'],
outPath=R['FolderName'],
yaxis_scale=True)
saveData.save_test_point_wise_err2mat(point_square_error,
actName=act_func,
outPath=R['FolderName'])
plotData.plot_Hot_point_wise_err(point_square_error,
size_vec2mat=size2test,
actName=act_func,
seedNo=R['seed'],
outPath=R['FolderName'])
def solve_Multiscale_PDE(R):
log_out_path = R['FolderName'] # 将路径从字典 R 中提取出来
if not os.path.exists(log_out_path): # 判断路径是否已经存在
os.mkdir(log_out_path) # 无 log_out_path 路径，创建一个 log_out_path 路径
logfile_name = '%s_%s.txt' % ('logTrain', R['name2act_hidden'])
log_fileout = open(os.path.join(log_out_path, logfile_name), 'w') # 在这个路径下创建并打开一个可写的 log_train.txt文件
DNN_Log_Print.dictionary_out2file(R, log_fileout)
# 一般 laplace 问题需要的设置
batchsize_it = R['batch_size2interior']
batchsize_bd = R['batch_size2boundary']
bd_penalty_init = R['init_boundary_penalty'] # Regularization parameter for boundary conditions
penalty2WB = R['penalty2weight_biases'] # Regularization parameter for weights and biases
lr_decay = R['learning_rate_decay']
learning_rate = R['learning_rate']
hidden_layers = R['hidden_layers']
act_func = R['name2act_hidden']
# ------- set the problem ---------
input_dim = R['input_dim']
out_dim = R['output_dim']
region_l = 0.0
region_r = 1.0
if R['PDE_type'] == 'general_Laplace':
# -laplace u = f
region_l = 0.0
region_r = 1.0
f, u_true, u_left, u_right = General_Laplace.get_infos2Laplace_1D(
input_dim=input_dim, out_dim=out_dim, intervalL=region_l, intervalR=region_r, equa_name=R['equa_name'])
elif R['PDE_type'] == 'pLaplace':
# 求解如下方程, A_eps(x) 震荡的比较厉害，具有多个尺度
# d **** d ****
# - ---- | A_eps(x)* ---- u_eps(x) | =f(x), x \in R^n
# dx **** dx ****
# 问题区域，每个方向设置为一样的长度。等网格划分，对于二维是方形区域
p_index = R['order2pLaplace_operator']
epsilon = R['epsilon']
region_l = 0.0
region_r = 1.0
if R['equa_name'] == 'multi_scale':
u_true, f, A_eps, u_left, u_right = MS_LaplaceEqs.get_infos2pLaplace_1D(
in_dim=input_dim, out_dim=out_dim, intervalL=region_l, intervalR=region_r, index2p=p_index, eps=epsilon)
elif R['equa_name'] == '3scale2':
epsilon2 = 0.01
u_true, A_eps, u_left, u_right = MS_LaplaceEqs.get_infos2pLaplace_1D_3scale2(
in_dim=input_dim, out_dim=out_dim, intervalL=region_l, intervalR=region_r, index2p=p_index, eps1=epsilon,
eps2=epsilon2)
elif R['equa_name'] == 'rand_ceof':
num2sun_term = 2
Alpha = 1.2
Xi1 = [-0.25, 0.25]
Xi2 = [-0.3, 0.3]
# Xi1 = np.random.uniform(-0.5, 0.5, num2sun_term)
print('Xi1:', Xi1)
print('\n')
# Xi2 = np.random.uniform(-0.5, 0.5, num2sun_term)
print('Xi2:', Xi2)
print('\n')
u_left, u_right = random2pLaplace.random_boundary()
elif R['equa_name'] == 'rand_sin_ceof':
Xi1=-0.25
Xi2=0.25
u_true, f, A_eps = random2pLaplace.random_equa2()
elif R['PDE_type'] == 'Possion_Boltzmann':
# 求解如下方程, A_eps(x) 震荡的比较厉害，具有多个尺度
# d **** d ****
# - ---- | A_eps(x)* ---- u_eps(x) | + K(x)u_eps(x) =f(x), x \in R^n
# dx **** dx ****
p_index = R['order2pLaplace_operator']
epsilon = R['epsilon']
region_l = 0.0
region_r = 1.0
A_eps, kappa, u_true, u_left, u_right, f = MS_BoltzmannEqs.get_infos2Boltzmann_1D(
in_dim=input_dim, out_dim=out_dim, region_a=region_l, region_b=region_r, index2p=p_index, eps=epsilon,
eqs_name=R['equa_name'])
# 初始化权重和和偏置
flag1 = 'WB'
if R['model2NN'] == 'DNN_FourierBase':
Weights, Biases = DNN_base.Xavier_init_NN_Fourier(input_dim, out_dim, hidden_layers, flag1)
else:
Weights, Biases = DNN_base.Xavier_init_NN(input_dim, out_dim, hidden_layers, flag1)
global_steps = tf.compat.v1.Variable(0, trainable=False)
with tf.device('/gpu:%s' % (R['gpuNo'])):
with tf.compat.v1.variable_scope('vscope', reuse=tf.compat.v1.AUTO_REUSE):
X_it = tf.compat.v1.placeholder(tf.float32, name='X_it', shape=[None, input_dim]) # * 行 1 列
X_left = tf.compat.v1.placeholder(tf.float32, name='X_left', shape=[None, input_dim]) # * 行 1 列
X_right = tf.compat.v1.placeholder(tf.float32, name='X_right', shape=[None, input_dim]) # * 行 1 列
bd_penalty = tf.compat.v1.placeholder_with_default(input=1e3, shape=[], name='bd_p')
in_learning_rate = tf.compat.v1.placeholder_with_default(input=1e-5, shape=[], name='lr')
# 供选择的网络模式
if R['model2NN'] == 'DNN':
UNN = DNN_base.DNN(X_it, Weights, Biases, hidden_layers, activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'], activateOut_name=R['activateOut_func'])
UNN_left = DNN_base.DNN(X_left, Weights, Biases, hidden_layers, activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'], activateOut_name=R['name2act_out'])
UNN_right = DNN_base.DNN(X_right, Weights, Biases, hidden_layers, activateIn_name=R['name2act_in'],
activate_name=R['name2act_hidden'], activateOut_name=R['name2act_out'])
elif R['model2NN'] == 'DNN_scale':
freqs = R['freq']
UNN = DNN_base.DNN_scale(X_it, Weights, Biases, hidden_layers, freqs, activateIn_name=R['name2act_in'],
activate_name=act_func, activateOut_name=R['name2act_out'])
UNN_left = DNN_base.DNN_scale(X_left, Weights, Biases, hidden_layers, freqs,
activateIn_name=R['name2act_in'], activate_name=R['name2act_hidden'],
activateOut_name=R['name2act_out'])
UNN_right = DNN_base.DNN_scale(X_right, Weights, Biases, hidden_layers, freqs,
activateIn_name=R['name2act_in'], activate_name=R['name2act_hidden'],
activateOut_name=R['name2act_out'])
elif R['model2NN'] == 'DNN_FourierBase':
freqs = R['freq']
UNN = DNN_base.DNN_FourierBase(X_it, Weights, Biases, hidden_layers, freqs,
activate_name=act_func, activateOut_name=R['name2act_out'],
sFourier=R['sfourier'])
UNN_left = DNN_base.DNN_FourierBase(X_left, Weights, Biases, hidden_layers, freqs,
activate_name=act_func, activateOut_name=R['name2act_out'],
sFourier=R['sfourier'])
UNN_right = DNN_base.DNN_FourierBase(X_right, Weights, Biases, hidden_layers, freqs,
activate_name=act_func, activateOut_name=R['name2act_out'],
sFourier=R['sfourier'])
# 变分形式的loss of interior，训练得到的 UNN 是 * 行 1 列
if R['loss_type'] == 'variational_loss':
dUNN = tf.gradients(UNN, X_it)
if R['PDE_type'] == 'general_Laplace':
dUNN_Norm = tf.reduce_sum(tf.square(dUNN), axis=-1)
loss_it_variational = (1.0 / 2) * tf.reshape(dUNN_Norm, shape=[-1, 1]) - \
tf.multiply(tf.reshape(f(X_it), shape=[-1, 1]), UNN)
elif R['PDE_type'] == 'pLaplace':
if R['equa_name'] == '3scale2':
a_eps = A_eps(X_it) # * 行 1 列
AdUNN_pNorm = tf.reduce_sum(a_eps * tf.pow(tf.abs(dUNN), p_index), axis=-1)
fx = MS_LaplaceEqs.force_sice_3scale2(X_it, eps1=R['epsilon'], eps2=0.01)
loss_it_variational = (1.0 / p_index) * tf.reshape(AdUNN_pNorm, shape=[-1, 1]) - \
tf.multiply(tf.reshape(fx, shape=[-1, 1]), UNN)
elif R['equa_name'] == 'rand_ceof':
a_eps = random2pLaplace.rangdom_ceof(x=X_it, xi1=Xi1, xi2=Xi2, K=num2sun_term, alpha=Alpha)
# fx = random2pLaplace.rangdom_force(x=X_it, xi1=Xi1, xi2=Xi2, K=num2sun_term, alpha=Alpha)
# duf = tf.gradients(force_side, X_it)
fx = random2pLaplace.rangdom_diff_force2x(x=X_it, xi1=Xi1, xi2=Xi2, K=num2sun_term, alpha=Alpha)
AdUNN_pNorm = tf.reduce_sum(a_eps * tf.pow(tf.abs(dUNN), p_index), axis=-1)
loss_it_variational = (1.0 / p_index) * tf.reshape(AdUNN_pNorm, shape=[-1, 1]) - \
tf.multiply(tf.reshape(fx, shape=[-1, 1]), UNN)
elif R['equa_name'] == 'rand_sin_ceof':
a_eps = 1.0
fx = random2pLaplace.random_sin_f(x=X_it, xi1=Xi1, xi2=Xi2, K=2, alpha=1.0)
AdUNN_pNorm = tf.reduce_sum(a_eps * tf.pow(tf.abs(dUNN), p_index), axis=-1)
loss_it_variational = (1.0 / p_index) * tf.reshape(AdUNN_pNorm, shape=[-1, 1]) - \
tf.multiply(tf.reshape(fx, shape=[-1, 1]), UNN)
else:
# a_eps = A_eps(X_it) # * 行 1 列
a_eps = 1 / (2 + tf.cos(2 * np.pi * X_it / epsilon))
AdUNN_pNorm = tf.reduce_sum(a_eps * tf.pow(tf.abs(dUNN), p_index), axis=-1)
loss_it_variational = (1.0 / p_index) * tf.reshape(AdUNN_pNorm, shape=[-1, 1]) - \
tf.multiply(tf.reshape(f(X_it), shape=[-1, 1]), UNN)
elif R['PDE_type'] == 'Possion_Boltzmann':
# a_eps = A_eps(X_it) # * 行 1 列
a_eps = 1 / (2 + tf.cos(2 * np.pi * X_it / epsilon))
Kappa = kappa(X_it)
AdUNN_pNorm = tf.reduce_sum(a_eps * tf.pow(tf.abs(dUNN), p_index), axis=-1)
if R['equa_name'] == 'Boltzmann2':
fside = MS_BoltzmannEqs.get_force_side2Boltzmann_1D(X_it, index2p=p_index, eps=epsilon)
else:
fside = tf.reshape(f(X_it), shape=[-1, 1])
if p_index == 1:
loss_it_variational = (1.0 / 2) * (tf.reshape(AdUNN_pNorm, shape=[-1, 1]) +
Kappa*UNN*UNN) - tf.multiply(fside, UNN)
elif p_index == 2:
loss_it_variational = (1.0 / 2) * (tf.reshape(AdUNN_pNorm, shape=[-1, 1]) +
Kappa*UNN*UNN*UNN) - tf.multiply(fside, UNN)
loss_it = tf.reduce_mean(loss_it_variational)
elif R['loss_type'] == 'L2_loss':
dUNN = tf.gradients(UNN, X_it)
if R['PDE_type'] == 'general_Laplace':
ddUNN = tf.gradients(dUNN, X_it)
loss_it_L2 = -1.0*ddUNN - tf.reshape(f(X_it), shape=[-1, 1])
square_loss_it = tf.square(loss_it_L2)
elif R['PDE_type'] == 'pLaplace':
a_eps = A_eps(X_it)
# a_eps = 1 / (2 + tf.cos(2 * np.pi * X_it / epsilon))
if p_index == 2.0:
AdUNNpNorm = 1.0*a_eps
elif p_index == 3.0:
dUNNp_2Nrom = tf.abs(dUNN)
AdUNNpNorm = tf.multiply(a_eps, dUNNp_2Nrom)
else:
dUNNp_2Nrom = tf.pow(tf.abs(dUNN), p_index-2.0)
AdUNNpNorm = tf.multiply(a_eps, dUNNp_2Nrom)
AdUNNpNorm_dUNN = tf.multiply(AdUNNpNorm, dUNN)
dAdUNNpNorm_dUNN = tf.gradients(AdUNNpNorm_dUNN, X_it)
if R['equa_name'] == '3scale2':
fx = MS_LaplaceEqs.force_sice_3scale2(X_it, eps1=R['epsilon'], eps2=0.01)
loss_it_L2 = dAdUNNpNorm_dUNN + tf.reshape(fx, shape=[-1, 1])
else:
loss_it_L2 = dAdUNNpNorm_dUNN + tf.reshape(f(X_it), shape=[-1, 1])
square_loss_it = tf.square(loss_it_L2)
elif R['PDE_type'] == 'Possion_Boltzmann':
a_eps = A_eps(X_it)
# a_eps = 1 / (2 + tf.cos(2 * np.pi * X_it / epsilon))
Kappa = kappa(X_it)
if p_index == 2.0:
AdUNNpNorm = 1.0*a_eps
elif p_index == 3.0:
dUNNp_2Nrom = tf.abs(dUNN)
AdUNNpNorm = tf.multiply(a_eps, dUNNp_2Nrom)
else:
dUNNp_2Nrom = tf.pow(tf.abs(dUNN), p_index-2.0)
AdUNNpNorm = tf.multiply(a_eps, dUNNp_2Nrom)
AdUNNpNorm_dUNN = tf.multiply(AdUNNpNorm, dUNN)
dAdUNNpNorm_dUNN = tf.gradients(AdUNNpNorm_dUNN, X_it)
loss_it_L2 = -1.0*dAdUNNpNorm_dUNN + Kappa*UNN - tf.reshape(f(X_it), shape=[-1, 1])
square_loss_it = tf.square(loss_it_L2)
# loss_it = tf.reduce_mean(loss_it_L2)*(region_r-region_l)
loss_it = tf.reduce_mean(square_loss_it)
U_left = u_left(X_left)
U_right = u_right(X_right)
loss_bd_square = tf.square(UNN_left - U_left) + tf.square(UNN_right - U_right)
loss_bd = tf.reduce_mean(loss_bd_square)
if R['regular_wb_model'] == 'L1':
regularSum2WB = DNN_base.regular_weights_biases_L1(Weights, Biases) # 正则化权重和偏置 L1正则化
elif R['regular_wb_model'] == 'L2':
regularSum2WB = DNN_base.regular_weights_biases_L2(Weights, Biases) # 正则化权重和偏置 L2正则化
else:
regularSum2WB = tf.constant(0.0) # 无正则化权重参数
PWB = penalty2WB * regularSum2WB
loss = loss_it + bd_penalty * loss_bd + PWB # 要优化的loss function
my_optimizer = tf.compat.v1.train.AdamOptimizer(in_learning_rate)
if R['train_model'] == 'group3_training':
train_op1 = my_optimizer.minimize(loss_it, global_step=global_steps)
train_op2 = my_optimizer.minimize(loss_bd, global_step=global_steps)
train_op3 = my_optimizer.minimize(loss, global_step=global_steps)
train_my_loss = tf.group(train_op1, train_op2, train_op3)
elif R['train_model'] == 'group2_training':
train_op2 = my_optimizer.minimize(loss_bd, global_step=global_steps)
train_op3 = my_optimizer.minimize(loss, global_step=global_steps)
train_my_loss = tf.group(train_op2, train_op3)
elif R['train_model'] == 'union_training':
train_my_loss = my_optimizer.minimize(loss, global_step=global_steps)
# 训练上的真解值和训练结果的误差
if R['equa_name'] == 'rand_ceof':
U_true = random2pLaplace.rangdom_exact_solution_1(x=X_it, xi1=Xi1, xi2=Xi2, K=num2sun_term, alpha=Alpha)
mean_square_error = tf.reduce_mean(tf.square(U_true - dUNN))
residual_error = mean_square_error / tf.reduce_mean(tf.square(U_true))
else:
U_true = u_true(X_it)
mean_square_error = tf.reduce_mean(tf.square(U_true - UNN))
residual_error = mean_square_error / tf.reduce_mean(tf.square(U_true))
t0 = time.time()
loss_it_all, loss_bd_all, loss_all, train_mse_all, train_rel_all = [], [], [], [], [] # 空列表, 使用 append() 添加元素
test_mse_all, test_rel_all = [], []
testing_epoch = []
test_batch_size = 1000
test_x_bach = np.reshape(np.linspace(region_l, region_r, num=test_batch_size), [-1, 1])
# ConfigProto 加上allow_soft_placement=True就可以使用 gpu 了
config = tf.compat.v1.ConfigProto(allow_soft_placement=True) # 创建sess的时候对sess进行参数配置
config.gpu_options.allow_growth = True # True是让TensorFlow在运行过程中动态申请显存，避免过多的显存占用。
config.allow_soft_placement = True # 当指定的设备不存在时，允许选择一个存在的设备运行。比如gpu不存在，自动降到cpu上运行
with tf.compat.v1.Session(config=config) as sess:
sess.run(tf.compat.v1.global_variables_initializer())
tmp_lr = learning_rate
for i_epoch in range(R['max_epoch'] + 1):
x_it_batch = DNN_data.rand_it(batchsize_it, input_dim, region_a=region_l, region_b=region_r)
xl_bd_batch, xr_bd_batch = DNN_data.rand_bd_1D(batchsize_bd, input_dim, region_a=region_l, region_b=region_r)
tmp_lr = tmp_lr * (1 - lr_decay)
if R['activate_penalty2bd_increase'] == 1:
if i_epoch < int(R['max_epoch'] / 10):
temp_penalty_bd = bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 5):
temp_penalty_bd = 10 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 4):
temp_penalty_bd = 50 * bd_penalty_init
elif i_epoch < int(R['max_epoch'] / 2):
temp_penalty_bd = 100 * bd_penalty_init
elif i_epoch < int(3 * R['max_epoch'] / 4):
temp_penalty_bd = 200 * bd_penalty_init
else:
temp_penalty_bd = 500 * bd_penalty_init
else:
temp_penalty_bd = bd_penalty_init
_, loss_it_tmp, loss_bd_tmp, loss_tmp, train_mse_tmp, train_res_tmp, pwb = sess.run(
[train_my_loss, loss_it, loss_bd, loss, mean_square_error, residual_error, PWB],
feed_dict={X_it: x_it_batch, X_left: xl_bd_batch, X_right: xr_bd_batch,
in_learning_rate: tmp_lr, bd_penalty: temp_penalty_bd})
loss_it_all.append(loss_it_tmp)
loss_bd_all.append(loss_bd_tmp)
loss_all.append(loss_tmp)
train_mse_all.append(train_mse_tmp)
train_rel_all.append(train_res_tmp)
if i_epoch % 1000 == 0:
run_times = time.time() - t0
DNN_Log_Print.print_and_log_train_one_epoch(
i_epoch, run_times, tmp_lr, temp_penalty_bd, pwb, loss_it_tmp, loss_bd_tmp, loss_tmp, train_mse_tmp,
train_res_tmp, log_out=log_fileout)
# --------------------------- test network ----------------------------------------------
testing_epoch.append(i_epoch / 1000)
if R['equa_name'] == 'rand_ceof':
u_true2test, unn2test = sess.run([U_true, dUNN], feed_dict={X_it: test_x_bach})
else:
u_true2test, unn2test = sess.run([U_true, UNN], feed_dict={X_it: test_x_bach})
mse2test = np.mean(np.square(u_true2test - unn2test))
test_mse_all.append(mse2test)
res2test = mse2test / np.mean(np.square(u_true2test))
test_rel_all.append(res2test)
DNN_Log_Print.print_and_log_test_one_epoch(mse2test, res2test, log_out=log_fileout)
# ----------------------- save training results to mat files, then plot them ---------------------------------
saveData.save_trainLoss2mat_1actFunc(loss_it_all, loss_bd_all, loss_all, actName=act_func, outPath=R['FolderName'])
plotData.plotTrain_loss_1act_func(loss_it_all, lossType='loss_it', seedNo=R['seed'], outPath=R['FolderName'])
plotData.plotTrain_loss_1act_func(loss_bd_all, lossType='loss_bd', seedNo=R['seed'], outPath=R['FolderName'],
yaxis_scale=True)
plotData.plotTrain_loss_1act_func(loss_all, lossType='loss', seedNo=R['seed'], outPath=R['FolderName'])
saveData.save_train_MSE_REL2mat(train_mse_all, train_rel_all, actName=act_func, outPath=R['FolderName'])
plotData.plotTrain_MSE_REL_1act_func(train_mse_all, train_rel_all, actName=act_func, seedNo=R['seed'],
outPath=R['FolderName'], yaxis_scale=True)
# ---------------------- save testing results to mat files, then plot them --------------------------------
saveData.save_2testSolus2mat(u_true2test, unn2test, actName='utrue', actName1=act_func, outPath=R['FolderName'])
plotData.plot_2solutions2test(u_true2test, unn2test, coord_points2test=test_x_bach,
batch_size2test=test_batch_size, seedNo=R['seed'], outPath=R['FolderName'],
subfig_type=R['subfig_type'])
saveData.save_testMSE_REL2mat(test_mse_all, test_rel_all, actName=act_func, outPath=R['FolderName'])
plotData.plotTest_MSE_REL(test_mse_all, test_rel_all, testing_epoch, actName=act_func,
seedNo=R['seed'], outPath=R['FolderName'], yaxis_scale=True)