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, hidden_units=(32, 32))
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=Generator2D(
(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, hidden_units=(32, 32))
solution_neural_net_heat, _ = solve2D(pde=heat,
condition=ibvp,
xy_min=(0, 0),
xy_max=(L, T),
net=net,
max_epochs=300,
train_generator=Generator2D(
(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.')