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pdebase.py
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import tensorflow as tf
import numpy as np
from matplotlib import pyplot as plt
from matplotlib import pyplot, cm
from mpl_toolkits.mplot3d import Axes3D
#from drawnow import drawnow, figure
def assert_shape(x, shape):
S = x.get_shape().as_list()
if len(S)!=len(shape):
raise Exception("Shape mismatch: {} -- {}".format(S, shape))
for i in range(len(S)):
if S[i]!=shape[i]:
raise Exception("Shape mismatch: {} -- {}".format(S, shape))
def compute_delta(u, x):
grad = tf.gradients(u, x)[0]
g1 = tf.gradients(grad[:,0], x)[0]
g2 = tf.gradients(grad[:,1], x)[0]
delta = g1[:,0] + g2[:,1]
assert_shape(delta, (None,))
return delta
def compute_delta_nd(u, x, n):
grad = tf.gradients(u, x)[0]
g1 = tf.gradients(grad[:, 0], x)[0]
delta = g1[:,0]
for i in range(1,n):
g = tf.gradients(grad[:,i], x)[0]
delta += g[:,i]
assert_shape(delta, (None,))
return delta
def compute_dx(u,x):
grad = tf.gradients(u, x)[0]
dudx = grad[:,0]
assert_shape(dudx, (None,))
return dudx
def compute_dy(u,x):
grad = tf.gradients(u, x)[0]
dudy = grad[:,1]
assert_shape(dudy, (None,))
return dudy
def rectspace(a,b,c,d,n):
x = np.linspace(a,b,n)
y = np.linspace(c,d,n)
[X,Y] = np.meshgrid(x,y)
return np.concatenate([X.reshape((-1, 1)), Y.reshape((-1, 1))], axis=1)
##
class NNPDE_ND:
def __init__(self,batch_size, N, d): # d- dimension, N-number of layers
self.d = d
self.batch_size = batch_size
self.N = N
self.x = tf.placeholder(tf.float64, (None, d)) # inner data
self.x_b = tf.placeholder(tf.float64, (None, d)) # boundary data
self.u_b = self.bsubnetwork(self.x_b, False)
self.u = self.bsubnetwork(self.x, True) + self.B(self.x) * self.subnetwork(self.x, False)
self.bloss = tf.reduce_sum((self.tfexactsol(self.x_b) - self.u_b) ** 2)
self.loss = self.loss_function()
var_list1 = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES, "boundary")
self.opt1 = tf.train.AdamOptimizer(learning_rate=0.001).minimize(self.bloss, var_list=var_list1)
var_list2 = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES, "inner")
self.opt2 = tf.train.AdamOptimizer(learning_rate=0.001).minimize(self.loss, var_list=var_list2)
self.init = tf.global_variables_initializer()
self.X_test = np.array([0.5]*self.d)[np.newaxis,:]
def tfexactsol(self, x):
raise NotImplementedError
def exactsol(self, x):
raise NotImplementedError
def B(self, x):
raise NotImplementedError
def f(self, x):
raise NotImplementedError
def subnetwork(self, x, reuse = False):
with tf.variable_scope("inner"):
for i in range(self.N):
x = tf.layers.dense(x, 256, activation=tf.nn.tanh, name="dense{}".format(i), reuse=reuse)
x = tf.layers.dense(x, 1, activation=None, name="last", reuse=reuse)
x = tf.squeeze(x, axis=1)
assert_shape(x, (None,))
return x
def bsubnetwork(self, x, reuse = False):
with tf.variable_scope("boundary"):
for i in range(self.N):
x = tf.layers.dense(x, 256, activation=tf.nn.tanh, name="bdense{}".format(i), reuse=reuse)
x = tf.layers.dense(x, 1, activation=None, name="blast", reuse=reuse)
x = tf.squeeze(x, axis=1)
assert_shape(x, (None,))
return x
def loss_function(self):
deltah = compute_delta_nd(self.u, self.x, self.d)
delta = self.f(self.x)
res = tf.reduce_sum((deltah - delta) ** 2)
assert_shape(res, ())
return res
def compute_L2(self, sess, x):
u0 = self.exactsol(x)
u1 = sess.run(self.u, feed_dict={self.x: x})[0]
return np.sqrt(np.mean((u0-u1)**2))
class NNPDE:
def __init__(self, batch_size, N, refn):
self.refn = refn # reference points
x = np.linspace(0, 1, refn)
y = np.linspace(0, 1, refn)
self.X, self.Y = np.meshgrid(x, y)
self.refnX = np.concatenate([self.X.reshape((-1, 1)), self.Y.reshape((-1, 1))], axis=1)
self.batch_size = batch_size # batchsize
self.N = N
self.x = tf.placeholder(tf.float64, (None, 2))
self.u = self.u_out(self.x)
self.loss = self.loss_function()
self.ploss = self.point_wise_loss()
self.fig = plt.figure()
self.opt = tf.train.AdamOptimizer(learning_rate=0.001).minimize(self.loss)
self.init = tf.global_variables_initializer()
def exactsol(self, x, y):
raise NotImplementedError
# data to be modified
def A(self, x):
raise NotImplementedError
def B(self, x):
raise NotImplementedError
def f(self, x):
raise NotImplementedError
def loss_function(self):
deltah = compute_delta(self.u, self.x)
delta = self.f(self.x)
res = tf.reduce_sum((deltah - delta) ** 2)
assert_shape(res, ())
return res
# end modification
def subnetwork(self, x):
for i in range(self.N):
x = tf.layers.dense(x, 256, activation=tf.nn.tanh)
x = tf.layers.dense(x, 1, activation=None, name="last")
x = tf.squeeze(x, axis=1)
return x
def u_out(self, x):
res = self.A(x) + self.B(x) * self.subnetwork(x)
assert_shape(res, (None,))
return res
def point_wise_loss(self):
deltah = compute_delta(self.u, self.x)
delta = self.f(self.x)
res = tf.abs(deltah - delta)
assert_shape(res, (None,))
return res
# def visualize(self, sess, showonlysol=False):
# x = np.linspace(0, 1, self.refn)
# y = np.linspace(0, 1, self.refn)
# [X, Y] = np.meshgrid(x, y)
# uh = sess.run(self.u, feed_dict={self.x: self.refnX})
# Z = uh.reshape((self.refn, self.refn))
# uhref = self.exactsol(X, Y)
# def draw():
# ax = self.fig.gca(projection='3d')
# if not showonlysol:
# ax.plot_surface(X, Y, uhref, rstride=1, cstride=1, cmap=cm.autumn,
# linewidth=0, antialiased=False, alpha=0.3)
# ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.summer,
# linewidth=0, antialiased=False, alpha=0.8)
# ax.set_xlim(0, 1)
# ax.set_ylim(0, 1)
# ax.set_zlim(0, 1.1)
# ax.set_xlabel('$x$')
# ax.set_ylabel('$y$')
# drawnow(draw)
# def visualize_point_wise_loss(self, sess):
# ploss = sess.run(self.ploss, feed_dict={self.x: self.refnX})
# x = np.linspace(0, 1, self.refn)
# y = np.linspace(0, 1, self.refn)
# [X, Y] = np.meshgrid(x, y)
# Z = ploss.reshape((self.refn, self.refn))
# def draw():
# ax = self.fig.gca(projection='3d')
# Z0 = np.log(Z + 1e-16) / np.log(10.0)
# Z0[Z0 < 1e-10] = 0
# ax.plot_surface(X, Y, Z0, rstride=1, cstride=1, cmap=cm.winter,
# linewidth=0, antialiased=False)
# ax.set_xlim(0, 1)
# ax.set_ylim(0, 1)
# ax.set_xlabel('$x$')
# ax.set_ylabel('$y$')
# drawnow(draw)
# def visualize_error(self, sess):
# x = np.linspace(0, 1, self.refn)
# y = np.linspace(0, 1, self.refn)
# [X, Y] = np.meshgrid(x, y)
# uh = sess.run(self.u, feed_dict={self.x: np.concatenate([X.reshape((-1, 1)), Y.reshape((-1, 1))], axis=1)})
# Z = uh.reshape((self.refn, self.refn))
# def draw():
# ax = self.fig.gca(projection='3d')
# ax.plot_surface(X, Y, self.exactsol(X, Y) - Z, rstride=1, cstride=1, cmap=cm.winter,
# linewidth=0, antialiased=False, alpha=0.85)
# ax.set_xlim(0, 1)
# ax.set_ylim(0, 1)
# ax.set_zlim(0, 1.1)
# ax.set_xlabel('$x$')
# ax.set_ylabel('$y$')
# drawnow(draw)
def train(self, sess, i=-1):
# self.X = rectspace(0,0.5,0.,0.5,self.n)
X = np.random.rand(self.batch_size, 2)
_, loss = sess.run([self.opt, self.loss], feed_dict={self.x: X})
if i % 10 == 0:
print("Iteration={}, loss= {}".format(i, loss))
# u(x;w_1, w_2) = A(x;w_1) + B(x) * N(x;w_2)
# L u(x;w_1, w_2) = L A(x;w_1) + L( B(x) * N(x;w_2) ) --> f
class NNPDE2:
def __init__(self, batch_size, N, refn):
self.rloss = []
self.rbloss = []
self.rl2 = []
self.refn = refn # reference points
x = np.linspace(0, 1, refn)
y = np.linspace(0, 1, refn)
self.X, self.Y = np.meshgrid(x, y)
self.refX = np.concatenate([self.X.reshape((-1, 1)), self.Y.reshape((-1, 1))], axis=1)
self.batch_size = batch_size # batchsize
self.N = N # number of dense layers
self.x = tf.placeholder(tf.float64, (None, 2)) # inner data
self.x_b = tf.placeholder(tf.float64, (None, 2)) # boundary data
self.u_b = self.bsubnetwork(self.x_b, False)
self.u = self.bsubnetwork(self.x, True) + self.B(self.x) * self.subnetwork(self.x, False)
self.bloss = tf.reduce_sum((self.tfexactsol(self.x_b)-self.u_b)**2)
self.loss = self.loss_function()
self.ploss = self.point_wise_loss()
var_list1 = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES, "boundary")
self.opt1 = tf.train.AdamOptimizer(learning_rate=0.001).minimize(self.bloss,var_list=var_list1)
var_list2 = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES, "inner")
self.opt2 = tf.train.AdamOptimizer(learning_rate=0.001).minimize(self.loss, var_list=var_list2)
self.init = tf.global_variables_initializer()
def B(self, x):
return x[:, 0] * (1 - x[:, 0]) * x[:, 1] * (1 - x[:, 1])
def exactsol(self, x, y):
raise NotImplementedError
def tfexactsol(self, x):
raise NotImplementedError
def f(self, x):
raise NotImplementedError
def loss_function(self):
deltah = compute_delta(self.u, self.x)
delta = self.f(self.x)
res = tf.reduce_sum((deltah - delta) ** 2)
assert_shape(res, ())
return res
# end modification
def subnetwork(self, x, reuse = False):
with tf.variable_scope("inner"):
for i in range(self.N):
x = tf.layers.dense(x, 256, activation=tf.nn.tanh, name="dense{}".format(i), reuse=reuse)
x = tf.layers.dense(x, 1, activation=None, name="last", reuse=reuse)
x = tf.squeeze(x, axis=1)
assert_shape(x, (None,))
return x
def bsubnetwork(self, x, reuse = False):
with tf.variable_scope("boundary"):
for i in range(self.N):
x = tf.layers.dense(x, 256, activation=tf.nn.tanh, name="bdense{}".format(i), reuse=reuse)
x = tf.layers.dense(x, 1, activation=None, name="blast", reuse=reuse)
x = tf.squeeze(x, axis=1)
assert_shape(x, (None,))
return x
def point_wise_loss(self):
deltah = compute_delta(self.u, self.x)
delta = self.f(self.x)
res = tf.abs(deltah - delta)
assert_shape(res, (None,))
return res
def plot_exactsol(self):
Z = self.exactsol(self.X, self.Y)
ax = self.fig.gca(projection='3d')
ax.plot_surface(self.X, self.Y, Z, rstride=1, cstride=1, cmap=cm.summer,
linewidth=0, antialiased=False, alpha=1.0)
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
# def visualize(self, sess, showonlysol=False, i=None, savefig=None):
# x = np.linspace(0, 1, self.refn)
# y = np.linspace(0, 1, self.refn)
# [X, Y] = np.meshgrid(x, y)
# uh = sess.run(self.u, feed_dict={self.x: self.refX})
# Z = uh.reshape((self.refn, self.refn))
# uhref = self.exactsol(X, Y)
# def draw():
# self.fig = plt.figure()
# ax = self.fig.gca(projection='3d')
# if not showonlysol:
# ax.plot_surface(X, Y, uhref, rstride=1, cstride=1, cmap=cm.autumn,
# linewidth=0, antialiased=False, alpha=0.3)
# ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.summer,
# linewidth=0, antialiased=False, alpha=0.5)
# ax.set_xlim(0, 1)
# ax.set_ylim(0, 1)
# ax.set_zlim(0, 1.1)
# ax.set_xlabel('$x$')
# ax.set_ylabel('$y$')
# if i:
# plt.title("Iteration {}".format(i))
# if savefig:
# plt.savefig("{}/fig{}".format(savefig,0 if i is None else i))
# drawnow(draw)
# def visualize_point_wise_loss(self, sess):
# ploss = sess.run(self.ploss, feed_dict={self.x: self.refnX})
# x = np.linspace(0, 1, self.refn)
# y = np.linspace(0, 1, self.refn)
# [X, Y] = np.meshgrid(x, y)
# Z = ploss.reshape((self.refn, self.refn))
# def draw():
# ax = self.fig.gca(projection='3d')
# Z0 = np.log(Z + 1e-16) / np.log(10.0)
# Z0[Z0 < 1e-10] = 0
# ax.plot_surface(X, Y, Z0, rstride=1, cstride=1, cmap=cm.winter,
# linewidth=0, antialiased=False)
# ax.set_xlim(0, 1)
# ax.set_ylim(0, 1)
# ax.set_xlabel('$x$')
# ax.set_ylabel('$y$')
# # drawnow(draw)
# draw()
# def visualize_error(self, sess):
# x = np.linspace(0, 1, self.refn)
# y = np.linspace(0, 1, self.refn)
# [X, Y] = np.meshgrid(x, y)
# uh = sess.run(self.u, feed_dict={self.x: np.concatenate([X.reshape((-1, 1)), Y.reshape((-1, 1))], axis=1)})
# Z = uh.reshape((self.refn, self.refn))
# def draw():
# ax = self.fig.gca(projection='3d')
# ax.plot_surface(X, Y, self.exactsol(X, Y) - Z, rstride=1, cstride=1, cmap=cm.winter,
# linewidth=0, antialiased=False, alpha=0.85)
# ax.set_xlim(0, 1)
# ax.set_ylim(0, 1)
# ax.set_zlim(0, 1.1)
# ax.set_xlabel('$x$')
# ax.set_ylabel('$y$')
# drawnow(draw)
def train(self, sess, i=-1):
# self.X = rectspace(0,0.5,0.,0.5,self.n)
bX = np.zeros((4*self.batch_size, 2))
bX[:self.batch_size,0] = np.random.rand(self.batch_size)
bX[:self.batch_size,1] = 0.0
bX[self.batch_size:2*self.batch_size, 0] = np.random.rand(self.batch_size)
bX[self.batch_size:2*self.batch_size, 1] = 1.0
bX[2*self.batch_size:3*self.batch_size, 0] = 0.0
bX[2*self.batch_size:3*self.batch_size, 1] = np.random.rand(self.batch_size)
bX[3*self.batch_size:4*self.batch_size, 0] = 1.0
bX[3 * self.batch_size:4 * self.batch_size, 1] = np.random.rand(self.batch_size)
bloss = sess.run([self.bloss], feed_dict={self.x_b: bX})[0]
# if the loss is small enough, stop training on the boundary
if bloss>1e-5:
for _ in range(5):
_, bloss = sess.run([self.opt1, self.bloss], feed_dict={self.x_b: bX})
X = np.random.rand(self.batch_size, 2)
_, loss = sess.run([self.opt2, self.loss], feed_dict={self.x: X})
########## record loss ############
self.rbloss.append(bloss)
self.rloss.append(loss)
uh = sess.run(self.u, feed_dict={self.x: self.refX})
Z = uh.reshape((self.refn, self.refn))
uhref = self.exactsol(self.X, self.Y)
self.rl2.append( np.sqrt(np.mean((Z-uhref)**2)) )
########## record loss ############
if i % 10 == 0:
print("Iteration={}, bloss = {}, loss= {}, L2={}".format(i, bloss, loss, self.rl2[-1]))