def test_pidon_operator_on_spherical_pde():
set_random_seed(0)
diff_eq = DiffusionEquation(3)
mesh = Mesh(
[(1., 11.), (0., 2 * np.pi), (.25 * np.pi, .75 * np.pi)],
[2., np.pi / 5., np.pi / 4],
CoordinateSystem.SPHERICAL)
bcs = [
(DirichletBoundaryCondition(
lambda x, t: np.ones((len(x), 1)), is_static=True),
DirichletBoundaryCondition(
lambda x, t: np.full((len(x), 1), 1. / 11.), is_static=True)),
(NeumannBoundaryCondition(
lambda x, t: np.zeros((len(x), 1)), is_static=True),
NeumannBoundaryCondition(
lambda x, t: np.zeros((len(x), 1)), is_static=True)),
(NeumannBoundaryCondition(
lambda x, t: np.zeros((len(x), 1)), is_static=True),
NeumannBoundaryCondition(
lambda x, t: np.zeros((len(x), 1)), is_static=True))
]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
ic = ContinuousInitialCondition(cp, lambda x: 1. / x[:, :1])
t_interval = (0., .5)
ivp = InitialValueProblem(cp, t_interval, ic)
sampler = UniformRandomCollocationPointSampler()
pidon = PIDONOperator(sampler, .001, True)
training_loss_history, test_loss_history = pidon.train(
cp,
t_interval,
training_data_args=DataArgs(
y_0_functions=[ic.y_0],
n_domain_points=20,
n_boundary_points=10,
n_batches=1
),
model_args=ModelArgs(
latent_output_size=20,
branch_hidden_layer_sizes=[30, 30],
trunk_hidden_layer_sizes=[30, 30],
),
optimization_args=OptimizationArgs(
optimizer=optimizers.Adam(learning_rate=2e-5),
epochs=3,
verbose=False
)
)
assert len(training_loss_history) == 3
for i in range(2):
assert np.all(
training_loss_history[i + 1].weighted_total_loss.numpy() <
training_loss_history[i].weighted_total_loss.numpy())
solution = pidon.solve(ivp)
assert solution.d_t == .001
assert solution.discrete_y().shape == (500, 6, 11, 3, 1)
def test_beta_initial_condition_with_wrong_number_of_alpha_and_betas():
diff_eq = DiffusionEquation(1)
mesh = Mesh([(0., 1.)], [.1])
bcs = [(NeumannBoundaryCondition(lambda x: np.zeros((len(x), 1))), ) * 2]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
with pytest.raises(ValueError):
BetaInitialCondition(cp, [(1., 1.), (1., 1)])
def test_continuous_initial_condition_1d_pde():
diff_eq = DiffusionEquation(1)
mesh = Mesh([(0., 20.)], [.1])
bcs = [(DirichletBoundaryCondition(lambda x, t: np.zeros((len(x), 1)),
is_static=True),
DirichletBoundaryCondition(lambda x, t: np.full((len(x), 1), 1.5),
is_static=True))]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
initial_condition = ContinuousInitialCondition(
cp, lambda x: np.exp(-np.square(np.array(x) - 10.) / (2 * 5**2)))
assert np.isclose(initial_condition.y_0(np.full((1, 1), 10.)), 1.)
assert np.isclose(
initial_condition.y_0(np.full((1, 1),
np.sqrt(50) + 10.)), np.e**-1)
assert np.allclose(initial_condition.y_0(np.full((5, 1), 10.)),
np.ones((5, 1)))
y_0_vertices = initial_condition.discrete_y_0(True)
assert y_0_vertices.shape == (201, 1)
assert y_0_vertices[0, 0] == 0.
assert y_0_vertices[-1, 0] == 1.5
assert y_0_vertices[100, 0] == 1.
assert np.all(0. < y_0_vertices[1:100, 0]) \
and np.all(y_0_vertices[1:100, 0] < 1.)
assert np.all(0. < y_0_vertices[101:-1, 0]) \
and np.all(y_0_vertices[101:-1, 0] < 1.)
y_0_cell_centers = initial_condition.discrete_y_0(False)
assert y_0_cell_centers.shape == (200, 1)
assert np.all(0. < y_0_cell_centers) and np.all(y_0_cell_centers < 1.)
def test_beta_initial_condition_with_more_than_1d_pde():
diff_eq = DiffusionEquation(2)
mesh = Mesh([(0., 1.), (0., 1.)], [.1, .1])
bcs = [(NeumannBoundaryCondition(lambda x: np.zeros((len(x), 1))), ) * 2
] * 2
cp = ConstrainedProblem(diff_eq, mesh, bcs)
with pytest.raises(ValueError):
BetaInitialCondition(cp, [(1., 1.), (1., 1)])
def test_ode_operator_on_pde():
diff_eq = DiffusionEquation(1, 1.5)
mesh = Mesh([(0., 10.)], [.1])
bcs = [
(NeumannBoundaryCondition(lambda x, t: np.zeros((len(x), 1))),
DirichletBoundaryCondition(lambda x, t: np.zeros((len(x), 1)))),
]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
ic = GaussianInitialCondition(cp, [(np.array([5.]), np.array([[2.5]]))],
[20.])
ivp = InitialValueProblem(cp, (0., 10.), ic)
op = ODEOperator('RK23', 2.5e-3)
with pytest.raises(ValueError):
op.solve(ivp)
def test_cp_pde_with_wrong_boundary_constraint_length():
diff_eq = DiffusionEquation(2)
mesh = Mesh([(0., 5.), (-5., 5.)], [.1, .2])
static_bcs = [(DirichletBoundaryCondition(lambda x, t: np.zeros((13, 1)),
is_static=True), ) * 2] * 2
with pytest.raises(ValueError):
ConstrainedProblem(diff_eq, mesh, static_bcs)
dynamic_bcs = [
(DirichletBoundaryCondition(lambda x, t: np.zeros((13, 1))), ) * 2
] * 2
cp = ConstrainedProblem(diff_eq, mesh, dynamic_bcs)
with pytest.raises(ValueError):
cp.create_boundary_constraints(True, 0.)
def test_fdm_operator_on_spherical_pde():
diff_eq = DiffusionEquation(3)
mesh = Mesh([(1., 11.), (0., 2. * np.pi), (.1 * np.pi, .9 * np.pi)],
[2., np.pi / 5., np.pi / 5], CoordinateSystem.SPHERICAL)
bcs = [(NeumannBoundaryCondition(lambda x, t: np.zeros((len(x), 1)),
is_static=True),
NeumannBoundaryCondition(lambda x, t: np.zeros((len(x), 1)),
is_static=True))] * 3
cp = ConstrainedProblem(diff_eq, mesh, bcs)
ic = ContinuousInitialCondition(cp, lambda x: 1. / x[:, :1])
ivp = InitialValueProblem(cp, (0., 5.), ic)
op = FDMOperator(RK4(), ThreePointCentralDifferenceMethod(), .1)
solution = op.solve(ivp)
assert solution.vertex_oriented
assert solution.d_t == .1
assert solution.discrete_y().shape == (50, 6, 11, 5, 1)
assert solution.discrete_y(False).shape == (50, 5, 10, 4, 1)
def test_cp_1d_pde():
diff_eq = DiffusionEquation(1)
mesh = Mesh([(0., 1.)], [.1])
bcs = [(NeumannBoundaryCondition(lambda x, t: np.zeros((1, 1)),
is_static=True), ) * 2]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
assert cp.are_all_boundary_conditions_static
assert not cp.are_there_boundary_conditions_on_y
assert cp.y_shape(True) == (11, 1)
assert cp.y_shape(False) == (10, 1)
assert cp.differential_equation == diff_eq
assert cp.mesh == mesh
assert np.array_equal(cp.boundary_conditions, bcs)
y_vertex_constraints = cp.static_y_vertex_constraints
assert y_vertex_constraints.shape == (1, )
assert np.all(y_vertex_constraints[0].mask == [False])
assert np.all(y_vertex_constraints[0].values == [])
vertex_boundary_constraints = cp.static_boundary_constraints(True)
y_vertex_boundary_constraints = vertex_boundary_constraints[0]
assert y_vertex_boundary_constraints.shape == (1, 1)
assert y_vertex_boundary_constraints[0, 0][0] is None
assert y_vertex_boundary_constraints[0, 0][1] is None
d_y_vertex_boundary_constraints = vertex_boundary_constraints[1]
assert d_y_vertex_boundary_constraints.shape == (1, 1)
assert np.all(d_y_vertex_boundary_constraints[0, 0][0].mask == [True])
assert np.all(d_y_vertex_boundary_constraints[0, 0][0].values == [0.])
assert np.all(d_y_vertex_boundary_constraints[0, 0][1].mask == [True])
assert np.all(d_y_vertex_boundary_constraints[0, 0][1].values == [0.])
cell_boundary_constraints = cp.static_boundary_constraints(False)
y_cell_boundary_constraints = cell_boundary_constraints[0]
assert y_cell_boundary_constraints.shape == (1, 1)
assert y_cell_boundary_constraints[0, 0][0] is None
assert y_cell_boundary_constraints[0, 0][1] is None
d_y_cell_boundary_constraints = cell_boundary_constraints[1]
assert d_y_cell_boundary_constraints.shape == (1, 1)
assert np.all(d_y_cell_boundary_constraints[0, 0][0].mask == [True])
assert np.all(d_y_cell_boundary_constraints[0, 0][0].values == [0.])
assert np.all(d_y_cell_boundary_constraints[0, 0][1].mask == [True])
assert np.all(d_y_cell_boundary_constraints[0, 0][1].values == [0.])
def test_fdm_operator_on_pde_with_dynamic_boundary_conditions():
diff_eq = DiffusionEquation(1, 1.5)
mesh = Mesh([(0., 10.)], [1.])
bcs = [
(NeumannBoundaryCondition(lambda x, t: np.zeros((len(x), 1))),
DirichletBoundaryCondition(lambda x, t: np.full((len(x), 1), t / 5.))
),
]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
ic = GaussianInitialCondition(cp, [(np.array([5.]), np.array([[2.5]]))],
[20.])
ivp = InitialValueProblem(cp, (0., 10.), ic)
op = FDMOperator(RK4(), ThreePointCentralDifferenceMethod(), .5)
solution = op.solve(ivp)
y = solution.discrete_y()
assert solution.vertex_oriented
assert solution.d_t == .5
assert y.shape == (20, 11, 1)
assert solution.discrete_y(False).shape == (20, 10, 1)
assert np.isclose(y[0, -1, 0], .1)
assert np.isclose(y[-1, -1, 0], 2.)
def test_parareal_operator_on_pde():
diff_eq = DiffusionEquation(2)
mesh = Mesh([(0., 5.), (0., 5.)], [1., 1.])
bcs = [(NeumannBoundaryCondition(lambda x, _: np.zeros((len(x), 1)),
is_static=True),
NeumannBoundaryCondition(lambda x, _: np.zeros((len(x), 1)),
is_static=True))] * 2
cp = ConstrainedProblem(diff_eq, mesh, bcs)
ic = GaussianInitialCondition(
cp, [(np.array([2.5, 2.5]), np.array([[1., 0.], [0., 1.]]))])
ivp = InitialValueProblem(cp, (0., 5.), ic)
f = FDMOperator(RK4(), ThreePointCentralDifferenceMethod(), .05)
g = FDMOperator(RK4(), ThreePointCentralDifferenceMethod(), .5)
p = PararealOperator(f, g, .005)
f_solution = f.solve(ivp)
p_solution = p.solve(ivp)
assert p_solution.vertex_oriented == f_solution.vertex_oriented
assert p_solution.d_t == f_solution.d_t
assert np.array_equal(p_solution.t_coordinates, f_solution.t_coordinates)
assert np.allclose(p_solution.discrete_y(), f_solution.discrete_y())
def test_pidon_operator_in_ar_mode_training_with_dynamic_boundary_conditions():
diff_eq = DiffusionEquation(1, .25)
mesh = Mesh([(0., .5)], (.05,))
bcs = [
(NeumannBoundaryCondition(
lambda x, t: np.full((len(x), 1), t), is_static=False),
NeumannBoundaryCondition(
lambda x, t: np.zeros((len(x), 1)), is_static=True)),
]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
t_interval = (0., .5)
y_0_functions = [lambda x: np.zeros((len(x), 1))]
pidon = PIDONOperator(UniformRandomCollocationPointSampler(), .001, True)
with pytest.raises(ValueError):
pidon.train(
cp,
t_interval,
training_data_args=DataArgs(
y_0_functions=y_0_functions,
n_domain_points=50,
n_boundary_points=20,
n_batches=2
),
model_args=ModelArgs(
latent_output_size=50,
branch_hidden_layer_sizes=[50, 50],
trunk_hidden_layer_sizes=[50, 50],
),
optimization_args=OptimizationArgs(
optimizer={'class_name': 'Adam'},
epochs=3,
ic_loss_weight=10.,
verbose=False
)
)
def test_fdm_operator_conserves_density_on_zero_flux_diffusion_equation():
diff_eq = DiffusionEquation(1, 5.)
mesh = Mesh([(0., 500.)], [.1])
bcs = [
(NeumannBoundaryCondition(lambda x, t: np.zeros((len(x), 1)),
is_static=True),
NeumannBoundaryCondition(lambda x, t: np.zeros((len(x), 1)),
is_static=True)),
]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
ic = GaussianInitialCondition(cp, [(np.array([250]), np.array([[250.]]))],
[1000.])
ivp = InitialValueProblem(cp, (0., 20.), ic)
y_0 = ic.discrete_y_0(True)
y_0_sum = np.sum(y_0)
fdm_op = FDMOperator(CrankNicolsonMethod(),
ThreePointCentralDifferenceMethod(), 1e-3)
solution = fdm_op.solve(ivp)
y = solution.discrete_y()
y_sums = np.sum(y, axis=tuple(range(1, y.ndim)))
assert np.allclose(y_sums, y_0_sum)
def test_pidon_operator_on_pde_with_dynamic_boundary_conditions():
set_random_seed(0)
diff_eq = DiffusionEquation(1, .25)
mesh = Mesh([(0., 1.)], (.1,))
bcs = [
(NeumannBoundaryCondition(lambda x, t: np.full((len(x), 1), t)),
NeumannBoundaryCondition(lambda x, t: np.full((len(x), 1), t))),
]
cp = ConstrainedProblem(diff_eq, mesh, bcs)
t_interval = (0., .5)
training_y_0_functions = [
BetaInitialCondition(cp, [(p, p)]).y_0 for p in [2., 3., 4., 5.]
]
test_y_0_functions = [
BetaInitialCondition(cp, [(p, p)]).y_0 for p in [2.5, 3.5, 4.5]
]
sampler = UniformRandomCollocationPointSampler()
pidon = PIDONOperator(sampler, .001, True)
training_loss_history, test_loss_history = pidon.train(
cp,
t_interval,
training_data_args=DataArgs(
y_0_functions=training_y_0_functions,
n_domain_points=50,
n_boundary_points=20,
n_batches=2
),
test_data_args=DataArgs(
y_0_functions=test_y_0_functions,
n_domain_points=25,
n_boundary_points=10,
n_batches=1
),
model_args=ModelArgs(
latent_output_size=50,
branch_hidden_layer_sizes=[50, 50],
trunk_hidden_layer_sizes=[50, 50],
),
optimization_args=OptimizationArgs(
optimizer={
'class_name': 'Adam',
'config': {
'learning_rate': 1e-4
}
},
epochs=3,
ic_loss_weight=10.,
verbose=False
)
)
assert len(training_loss_history) == 3
assert len(test_loss_history) == 3
for i in range(2):
assert training_loss_history[i + 1].weighted_total_loss.numpy() < \
training_loss_history[i].weighted_total_loss.numpy()
assert test_loss_history[i + 1].weighted_total_loss.numpy() < \
test_loss_history[i].weighted_total_loss.numpy()
ic = BetaInitialCondition(cp, [(3.5, 3.5)])
ivp = InitialValueProblem(cp, t_interval, ic)
solution = pidon.solve(ivp)
assert solution.d_t == .001
assert solution.discrete_y().shape == (500, 11, 1)