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def main():
def ide(x, y, int_mat):
rhs = tf.matmul(int_mat, y)
lhs1 = tf.gradients(y, x)[0]
return (lhs1 + y)[: tf.size(rhs)] - rhs
def kernel(x, s):
return np.exp(s - x)
def boundary(x, on_boundary):
return on_boundary and np.isclose(x[0], 0)
def func(x):
return np.exp(-x) * np.cosh(x)
geom = dde.geometry.Interval(0, 5)
bc = dde.DirichletBC(geom, func, boundary)
quad_deg = 20
data = dde.data.IDE(
geom,
ide,
bc,
quad_deg,
kernel=kernel,
num_domain=10,
num_boundary=2,
train_distribution="uniform",
)
layer_size = [1] + [20] * 3 + [1]
activation = "tanh"
def main():
def pde(x, y):
dy_x = tf.gradients(y, x)[0]
dy_xx = tf.gradients(dy_x, x)[0]
return -dy_xx - np.pi ** 2 * tf.sin(np.pi * x)
def boundary(x, on_boundary):
return on_boundary
def func(x):
return np.sin(np.pi * x)
geom = dde.geometry.Interval(-1, 1)
bc = dde.DirichletBC(geom, func, boundary)
data = dde.data.PDE(geom, 1, pde, bc, 16, 2, func=func, num_test=100)
layer_size = [1] + [50] * 3 + [1]
activation = "tanh"
initializer = "Glorot uniform"
net = dde.maps.FNN(layer_size, activation, initializer)
model = dde.Model(data, net)
model.compile("adam", lr=0.001, metrics=["l2 relative error"])
checkpointer = dde.callbacks.ModelCheckpoint(
"./model/model.ckpt", verbose=1, save_better_only=True
)
movie = dde.callbacks.MovieDumper(
"model/movie", [-1], [1], period=100, save_spectrum=True, y_reference=func
def main():
def pde(x, y):
dy_x = tf.gradients(y, x)[0]
dy_x, dy_t = dy_x[:, 0:1], dy_x[:, 1:]
dy_xx = tf.gradients(dy_x, x)[0][:, 0:1]
return (
dy_t
- dy_xx
+ tf.exp(-x[:, 1:])
* (tf.sin(np.pi * x[:, 0:1]) - np.pi ** 2 * tf.sin(np.pi * x[:, 0:1]))
)
def func(x):
return np.sin(np.pi * x[:, 0:1]) * np.exp(-x[:, 1:])
geom = dde.geometry.Interval(-1, 1)
timedomain = dde.geometry.TimeDomain(0, 1)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)
bc = dde.DirichletBC(geomtime, func, lambda _, on_boundary: on_boundary)
ic = dde.IC(geomtime, func, lambda _, on_initial: on_initial)
data = dde.data.TimePDE(
geomtime, 1, pde, [bc, ic], num_domain=40, func=func, num_test=10000
)
layer_size = [2] + [32] * 3 + [1]
activation = "tanh"
initializer = "Glorot uniform"
net = dde.maps.FNN(layer_size, activation, initializer)
net.outputs_modify(
lambda x, y: x[:, 1:2] * (1 - x[:, 0:1] ** 2) * y + tf.sin(np.pi * x[:, 0:1])
)
def main():
def func_lo(x):
A, B, C = 0.5, 10, -5
return A * (6 * x - 2) ** 2 * np.sin(12 * x - 4) + B * (x - 0.5) + C
def func_hi(x):
return (6 * x - 2) ** 2 * np.sin(12 * x - 4)
geom = dde.geometry.Interval(0, 1)
num_test = 1000
data = dde.data.MfFunc(geom, func_lo, func_hi, 100, 6, num_test)
activation = "tanh"
initializer = "Glorot uniform"
regularization = ["l2", 0.01]
net = dde.maps.MfNN(
[1] + [20] * 4 + [1],
[10] * 2 + [1],
activation,
initializer,
regularization=regularization,
)
model = dde.Model(data, net)
model.compile("adam", lr=0.001, metrics=["l2 relative error"])
def main():
def pde(x, y):
dy_x = tf.gradients(y, x)[0]
dy_xx = tf.gradients(dy_x, x)[0]
return -dy_xx - np.pi ** 2 * tf.sin(np.pi * x)
def boundary_l(x, on_boundary):
return on_boundary and np.isclose(x[0], -1)
def boundary_r(x, on_boundary):
return on_boundary and np.isclose(x[0], 1)
def func(x):
return np.sin(np.pi * x)
geom = dde.geometry.Interval(-1, 1)
bc1 = dde.DirichletBC(geom, func, boundary_l)
bc2 = dde.PeriodicBC(geom, 0, boundary_r)
data = dde.data.PDE(geom, 1, pde, [bc1, bc2], 16, 2, func=func, num_test=100)
layer_size = [1] + [50] * 3 + [1]
activation = "tanh"
initializer = "Glorot uniform"
net = dde.maps.FNN(layer_size, activation, initializer)
model = dde.Model(data, net)
model.compile("adam", lr=0.001, metrics=["l2 relative error"])
losshistory, train_state = model.train(epochs=10000)
dde.saveplot(losshistory, train_state, issave=True, isplot=True)