def BC_func(self, dim, geomtime):
if dim == 1:
bc = dde.NeumannBC(geomtime,
lambda x: np.zeros((len(x), 1)),
lambda _, on_boundary: on_boundary,
component=0)
elif dim == 2:
bc = dde.NeumannBC(geomtime,
lambda x: np.zeros((len(x), 1)),
self.boundary_func_2d,
component=0)
return bc
def main():
def pde(x, y):
dy_xx = dde.grad.hessian(y, x)
return dy_xx - 2
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 (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,
pde, [bc_l, bc_r],
16,
2,
solution=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)
def main():
def ddy(x, y):
dy_x = tf.gradients(y, x)[0]
return tf.gradients(dy_x, x)[0]
def dddy(x, y):
return tf.gradients(ddy(x, y), x)[0]
def pde(x, y):
dy_xxxx = tf.gradients(dddy(x, y), x)[0]
return dy_xxxx + 1
def boundary_l(x, on_boundary):
return on_boundary and np.isclose(x[0], 0)
def boundary_r(x, on_boundary):
return on_boundary and np.isclose(x[0], 1)
def func(x):
return -x ** 4 / 24 + x ** 3 / 6 - x ** 2 / 4
geom = dde.geometry.Interval(0, 1)
zero_func = lambda x: np.zeros((len(x), 1))
bc1 = dde.DirichletBC(geom, zero_func, boundary_l)
bc2 = dde.NeumannBC(geom, zero_func, boundary_l)
bc3 = dde.OperatorBC(geom, lambda x, y, _: ddy(x, y), boundary_r)
bc4 = dde.OperatorBC(geom, lambda x, y, _: dddy(x, y), boundary_r)
data = dde.data.PDE(
geom,
1,
pde,
[bc1, bc2, bc3, bc4],
num_domain=10,
num_boundary=2,
func=func,
num_test=100,
)
layer_size = [1] + [20] * 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)
return dy_xx - 2
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 (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, pde, [bc_l, bc_r], 16, 2, solution=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)