def test_monitor():
laplace = lambda u, x, y: diff(u, x, order=2) + diff(u, y, order=2)
bc = DirichletBVP2D(x_min=0,
x_min_val=lambda y: torch.sin(np.pi * y),
x_max=1,
x_max_val=lambda y: 0,
y_min=0,
y_min_val=lambda x: 0,
y_max=1,
y_max_val=lambda x: 0)
net = FCNN(n_input_units=2, n_hidden_units=32, n_hidden_layers=1)
solution_neural_net_laplace, _ = solve2D(
pde=laplace,
condition=bc,
xy_min=(0, 0),
xy_max=(1, 1),
net=net,
max_epochs=3,
train_generator=ExampleGenerator2D((32, 32), (0, 0), (1, 1),
method='equally-spaced-noisy'),
batch_size=64,
monitor=Monitor2D(check_every=1, xy_min=(0, 0), xy_max=(1, 1)))
print('Monitor test passed.')
def test_laplace():
laplace = lambda u, x, y: diff(u, x, order=2) + diff(u, y, order=2)
bc = DirichletBVP2D(x_min=0,
x_min_val=lambda y: torch.sin(np.pi * y),
x_max=1,
x_max_val=lambda y: 0,
y_min=0,
y_min_val=lambda x: 0,
y_max=1,
y_max_val=lambda x: 0)
net = FCNN(n_input_units=2, n_hidden_units=32, n_hidden_layers=1)
solution_neural_net_laplace, _ = solve2D(
pde=laplace,
condition=bc,
xy_min=(0, 0),
xy_max=(1, 1),
net=net,
max_epochs=300,
train_generator=ExampleGenerator2D((32, 32), (0, 0), (1, 1),
method='equally-spaced-noisy',
xy_noise_std=(0.01, 0.01)),
batch_size=64)
solution_analytical_laplace = lambda x, y: np.sin(np.pi * y) * np.sinh(
np.pi * (1 - x)) / np.sinh(np.pi)
xs, ys = np.linspace(0, 1, 101), np.linspace(0, 1, 101)
xx, yy = np.meshgrid(xs, ys)
sol_net = solution_neural_net_laplace(xx, yy, as_type='np')
sol_ana = solution_analytical_laplace(xx, yy)
assert isclose(sol_net, sol_ana, atol=0.01).all()
print('Laplace test passed.')
def test_legacy_module():
with warns(FutureWarning):
import neurodiffeq.generator
from neurodiffeq.ode import ExampleGenerator
from neurodiffeq.pde import ExampleGenerator2D, PredefinedExampleGenerator2D
from neurodiffeq.pde_spherical import ExampleGenerator3D, ExampleGeneratorSpherical
with warns(FutureWarning):
ExampleGenerator(100)
with warns(FutureWarning):
ExampleGenerator2D()
with warns(FutureWarning):
x = torch.rand(10)
y = torch.rand(10)
PredefinedExampleGenerator2D(x, y)
with warns(FutureWarning):
ExampleGenerator3D()
with warns(FutureWarning):
ExampleGeneratorSpherical(100)
def test_heat():
k, L, T = 0.3, 2, 3
heat = lambda u, x, t: diff(u, t) - k * diff(u, x, order=2)
ibvp = IBVP1D(x_min=0,
x_min_val=lambda t: 0,
x_max=L,
x_max_val=lambda t: 0,
t_min=0,
t_min_val=lambda x: torch.sin(np.pi * x / L))
net = FCNN(n_input_units=2, n_hidden_units=32, n_hidden_layers=1)
def mse(u, x, y):
true_u = torch.sin(np.pi * y) * torch.sinh(np.pi *
(1 - x)) / np.sinh(np.pi)
return torch.mean((u - true_u)**2)
solution_neural_net_heat, _ = solve2D(pde=heat,
condition=ibvp,
xy_min=(0, 0),
xy_max=(L, T),
net=net,
max_epochs=300,
train_generator=ExampleGenerator2D(
(32, 32), (0, 0), (L, T),
method='equally-spaced-noisy'),
batch_size=64,
metrics={'mse': mse})
solution_analytical_heat = lambda x, t: np.sin(np.pi * x / L) * np.exp(
-k * np.pi**2 * t / L**2)
xs = np.linspace(0, L, 101)
ts = np.linspace(0, T, 101)
xx, tt = np.meshgrid(xs, ts)
make_animation(solution_neural_net_heat, xs, ts) # test animation
sol_ana = solution_analytical_heat(xx, tt)
sol_net = solution_neural_net_heat(xx, tt, as_type='np')
assert isclose(sol_net, sol_ana, atol=0.01).all()
print('Heat test passed.')
def test_neumann_boundaries_2():
k, L, T = 0.3, 2, 3
heat = lambda u, x, t: diff(u, t) - k * diff(u, x, order=2)
solution_analytical_heat = lambda x, t: np.sin(np.pi * x / L) * np.exp(
-k * np.pi**2 * t / L**2)
# Neumann on the left Dirichlet on the right
ibvp = IBVP1D(
x_min=0,
x_min_prime=lambda t: np.pi / L * torch.exp(-k * np.pi**2 * t / L**2),
x_max=L,
x_max_val=lambda t: 0,
t_min=0,
t_min_val=lambda x: torch.sin(np.pi * x / L))
net = FCNN(n_input_units=2, n_hidden_units=32, n_hidden_layers=1)
solution_neural_net_heat, _ = solve2D(pde=heat,
condition=ibvp,
xy_min=(0, 0),
xy_max=(L, T),
net=net,
max_epochs=300,
train_generator=ExampleGenerator2D(
(32, 32), (0, 0), (L, T),
method='equally-spaced-noisy'),
batch_size=64)
xs = np.linspace(0, L, 101)
ts = np.linspace(0, T, 101)
xx, tt = np.meshgrid(xs, ts)
make_animation(solution_neural_net_heat, xs, ts) # test animation
sol_ana = solution_analytical_heat(xx, tt)
sol_net = solution_neural_net_heat(xx, tt, as_type='np')
assert isclose(sol_net, sol_ana, atol=0.1).all()
print('Neumann on the left Dirichlet on the right test passed.')