def get_solution(use_single: bool) -> Solution2D:
conditions = [
DirichletBVP2D(x0, ux0, x1, ux1, y0, uy0, y1, uy1),
DirichletBVP2D(x0, vx0, x1, vx1, y0, vy0, y1, vy1),
]
if use_single:
net = FCNN(2, 2)
for i, cond in enumerate(conditions):
cond.set_impose_on(i)
return Solution2D(net, conditions)
else:
nets = [FCNN(2, 1), FCNN(2, 1)]
return Solution2D(nets, conditions)
def test_dirichlet_bvp_2d():
# fix u(x, y) at the four corners (x0, y0), (x0, y1), (x1, y0), (x1, y1),
u00, u01, u10, u11 = [random.random() for _ in range(4)]
# set the boundary conditions on the four sides
net_f0, net_f1, net_g0, net_g1 = [FCNN(1, 1) for _ in range(4)]
cond_f0 = DirichletBVP(y0, u00, y1, u01)
cond_f1 = DirichletBVP(y0, u10, y1, u11)
cond_g0 = DirichletBVP(x0, u00, x1, u10)
cond_g1 = DirichletBVP(x0, u01, x1, u11)
f0 = lambda y: cond_f0.enforce(net_f0, y)
f1 = lambda y: cond_f1.enforce(net_f1, y)
g0 = lambda x: cond_g0.enforce(net_g0, x)
g1 = lambda x: cond_g1.enforce(net_g1, x)
# test whether condition is enforced
condition = DirichletBVP2D(x0, f0, x1, f1, y0, g0, y1, g1)
net = FCNN(2, 1)
x = x0 * ones
y = torch.linspace(y0, y1, ones.numel(), requires_grad=True).reshape(-1, 1)
assert all_close(condition.enforce(net, x, y), f0(y)), "left boundary not satisfied"
x = x1 * ones
y = torch.linspace(y0, y1, ones.numel(), requires_grad=True).reshape(-1, 1)
assert all_close(condition.enforce(net, x, y), f1(y)), "right boundary not satisfied"
x = torch.linspace(x0, x1, ones.numel(), requires_grad=True).reshape(-1, 1)
y = y0 * ones
assert all_close(condition.enforce(net, x, y), g0(x)), "lower boundary not satisfied"
x = torch.linspace(x0, x1, ones.numel(), requires_grad=True).reshape(-1, 1)
y = y1 * ones
assert all_close(condition.enforce(net, x, y), g1(x)), "upper boundary not satisfied"
def test_dirichlet_bvp_2d(x0, x1, y0, y1, u00, u01, u10, u11, ones, net21,
boundary_functions_2d):
# set the boundary conditions on the four sides
f0, f1, g0, g1 = boundary_functions_2d
# test whether condition is enforced
condition = DirichletBVP2D(x0, f0, x1, f1, y0, g0, y1, g1)
x = x0 * ones
y = torch.linspace(y0, y1, ones.numel(), requires_grad=True).reshape(-1, 1)
assert all_close(condition.enforce(net21, x, y),
f0(y)), "left boundary not satisfied"
x = x1 * ones
y = torch.linspace(y0, y1, ones.numel(), requires_grad=True).reshape(-1, 1)
assert all_close(condition.enforce(net21, x, y),
f1(y)), "right boundary not satisfied"
x = torch.linspace(x0, x1, ones.numel(), requires_grad=True).reshape(-1, 1)
y = y0 * ones
assert all_close(condition.enforce(net21, x, y),
g0(x)), "lower boundary not satisfied"
x = torch.linspace(x0, x1, ones.numel(), requires_grad=True).reshape(-1, 1)
y = y1 * ones
assert all_close(condition.enforce(net21, x, y),
g1(x)), "upper boundary not satisfied"
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, hidden_units=(32, 32))
solution_neural_net_laplace, loss_history = solve2D(
pde=laplace,
condition=bc,
xy_min=(0, 0),
xy_max=(1, 1),
net=net,
max_epochs=3,
train_generator=Generator2D((32, 32), (0, 0), (1, 1),
method='equally-spaced-noisy',
xy_noise_std=(0.01, 0.01)),
batch_size=64)
assert isinstance(solution_neural_net_laplace, Solution2D)
assert isinstance(loss_history, dict)
keys = ['train_loss', 'valid_loss']
for key in keys:
assert key in loss_history
assert isinstance(loss_history[key], list)
assert len(loss_history[keys[0]]) == len(loss_history[keys[1]])
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, hidden_units=(32, 32))
solution_neural_net_laplace, _ = solve2D(
pde=laplace, condition=bc, xy_min=(0, 0), xy_max=(1, 1),
net=net, max_epochs=3,
train_generator=Generator2D((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))
)
def test_train_generator():
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, hidden_units=(32, 32))
with pytest.raises(ValueError), pytest.warns(FutureWarning):
solution_neural_net_laplace, _ = solve2D(pde=laplace,
condition=bc,
net=net,
max_epochs=3,
batch_size=64)