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return on_boundary and np.isclose(x[0], 1)
def func(x):
return (x + 1) ** 2
geom = dde.geometry.Interval(-1, 1)
bc_l = dde.DirichletBC(geom, func, boundary_l)
bc_r = dde.RobinBC(geom, lambda X, y: y, boundary_r)
data = dde.data.PDE(geom, 1, pde, [bc_l, bc_r], 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)
col_x=(0,),
col_y=(1,),
)
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"])
losshistory, train_state = model.train(epochs=80000)
dde.saveplot(losshistory, train_state, issave=True, isplot=True)
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
)
losshistory, train_state = model.train(
epochs=10000, callbacks=[checkpointer, movie]
)
dde.saveplot(losshistory, train_state, issave=True, isplot=True)
# Plot PDE residue
x = geom.uniform_points(1000, True)
return on_boundary and np.isclose(x[0], 1)
def func(x):
return (x + 1) ** 2
geom = dde.geometry.Interval(-1, 1)
bc_l = dde.DirichletBC(geom, func, boundary_l)
bc_r = dde.NeumannBC(geom, lambda X: 2 * (X + 1), boundary_r)
data = dde.data.PDE(geom, 1, pde, [bc_l, bc_r], 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)
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])
)
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)
return -dy_xx - dy_yy - 1
def boundary(x, on_boundary):
return on_boundary
def func(x):
return np.zeros([len(x), 1])
geom = dde.geometry.Polygon([[0, 0], [1, 0], [1, -1], [-1, -1], [-1, 1], [0, 1]])
bc = dde.DirichletBC(geom, func, boundary)
data = dde.data.PDE(
geom, 1, pde, bc, num_domain=1200, num_boundary=120, num_test=1500
)
net = dde.maps.FNN([2] + [50] * 4 + [1], "tanh", "Glorot uniform")
model = dde.Model(data, net)
model.compile("adam", lr=0.001)
model.train(epochs=50000)
model.compile("L-BFGS-B")
losshistory, train_state = model.train()
dde.saveplot(losshistory, train_state, issave=True, isplot=True)
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)