def test_dirichlet_bvp_spherical():
r0, r1 = x0, x1
r2 = (r0 + r1) / 2
no_condition = NoCondition()
# B.C. for the interior boundary (r_min)
net_f = FCNN(2, 1)
f = lambda th, ph: no_condition.enforce(net_f, th, ph)
# B.C. for the exterior boundary (r_max)
net_g = FCNN(2, 1)
g = lambda th, ph: no_condition.enforce(net_g, th, ph)
condition = DirichletBVPSpherical(r_0=r0, f=f, r_1=r1, g=g)
net = FCNN(3, 1)
theta = torch.rand(N_SAMPLES, 1) * np.pi
phi = torch.rand(N_SAMPLES, 1) * 2 * np.pi
r = r0 * ones
assert all_close(condition.enforce(net, r, theta, phi),
f(theta, phi)), "inner Dirichlet BC not satisfied"
r = r1 * ones
assert all_close(condition.enforce(net, r, theta, phi),
g(theta, phi)), "inner Dirichlet BC not satisfied"
condition = DirichletBVPSpherical(r_0=r2, f=f)
r = r2 * ones
assert all_close(condition.enforce(net, r, theta, phi),
f(theta, phi)), "single ended BC not satisfied"
def test_no_condition():
N_INPUTS = 5
N_OUTPUTS = 5
for n_in, n_out in zip(range(1, N_INPUTS), range(1, N_OUTPUTS)):
xs = [torch.rand(N_SAMPLES, 1, requires_grad=True) for _ in range(n_in)]
net = FCNN(n_in, n_out)
cond = NoCondition()
y_cond = cond.enforce(net, *xs)
y_raw = net(torch.cat(xs, dim=1))
assert (y_cond == y_raw).all()
def solver():
return Solver1D(
ode_system=lambda u, t: [u + diff(u, t)],
conditions=[NoCondition()],
t_min=0.0,
t_max=1.0,
)
def test_monitor_2d(solution_style, history):
monitor = Monitor2D((0, 0), (1, 1),
check_every=100,
solution_style=solution_style)
nets = [FCNN(2, 1) for _ in range(N_FUNCTIONS)]
conditions = [NoCondition() for _ in range(N_FUNCTIONS)]
monitor.check(nets, conditions, history)
def test_legacy_max_degree_in_solution_spherical_harmonics():
with pytest.warns(FutureWarning):
SolutionSphericalHarmonics(
nets=[FCNN(1, 10)],
conditions=[NoCondition()],
max_degree=4,
)
def test_stream_plot_monitor(mask_fn, nx, ny, specify_field_names):
nets = [FCNN(2, 1, hidden_units=(3, )) for _ in range(5)]
conditions = [NoCondition() for _ in nets]
pairs = [(0, 1), (2, 3), (0, 3), 4, 2]
if specify_field_names:
field_names = [str(i) for i in range(len(pairs))]
else:
field_names = None
monitor = StreamPlotMonitor2D(
xy_min=(-1, -1),
xy_max=(1, 1),
nx=nx,
ny=ny,
pairs=pairs,
mask_fn=mask_fn,
equal_aspect=True,
field_names=field_names,
)
if specify_field_names:
with pytest.raises(ValueError):
StreamPlotMonitor2D(
xy_min=(-1, -1),
xy_max=(1, 1),
pairs=[0, 1],
field_names=['a', 'b', 'c'],
)
monitor.check(nets, conditions, history=None)
monitor.check(nets[::-1], conditions, history=None)
def test_inf_dirichlet_bvp_spherical():
r0 = random.random()
r1 = 1e15
no_condition = NoCondition()
net_f, net_g = FCNN(2, 1), FCNN(2, 1)
# B.C. for the interior boundary (r=r_min)
f = lambda th, ph: no_condition.enforce(net_f, th, ph)
# B.C. for the exterior boundary (r=infinity)
g = lambda th, ph: no_condition.enforce(net_g, th, ph)
net = FCNN(3, 1)
condition = InfDirichletBVPSpherical(r_0=r0, f=f, g=g, order=1)
theta = torch.rand(10, 1) * np.pi
phi = torch.rand(10, 1) * (2 * np.pi)
r = r0 * ones
assert all_close(condition.enforce(net, r, theta, phi), f(theta, phi)), "inner DirichletBC not satisfied"
r = r1 * ones
assert all_close(condition.enforce(net, r, theta, phi), g(theta, phi)), "Infinity DirichletBC not satisfied"
def test_train_generator_spherical():
pde = laplacian_spherical
condition = NoCondition()
train_generator = GeneratorSpherical(size=64,
r_min=0.,
r_max=1.,
method='equally-spaced-noisy')
r, th, ph = train_generator.get_examples()
assert (0. < r.min()) and (r.max() < 1.)
assert (0. <= th.min()) and (th.max() <= np.pi)
assert (0. <= ph.min()) and (ph.max() <= 2 * np.pi)
valid_generator = GeneratorSpherical(size=64,
r_min=1.,
r_max=1.,
method='equally-radius-noisy')
r, th, ph = valid_generator.get_examples()
assert (r == 1).all()
assert (0. <= th.min()) and (th.max() <= np.pi)
assert (0. <= ph.min()) and (ph.max() <= 2 * np.pi)
solve_spherical(pde,
condition,
0.0,
1.0,
train_generator=train_generator,
valid_generator=valid_generator,
max_epochs=1)
with raises(ValueError):
_ = GeneratorSpherical(64, method='bad_generator')
with raises(ValueError):
_ = GeneratorSpherical(64, r_min=-1.0)
with raises(ValueError):
_ = GeneratorSpherical(64, r_min=1.0, r_max=0.0)
def U(x):
cond = NoCondition()
nets = [FCNN(3, 1) for _ in range(3)]
return tuple(cond.enforce(net, *x) for net in nets)
def u(x):
cond = NoCondition()
net = FCNN(3, 1)
return cond.enforce(net, *x)
def scalar_field(x):
cond = NoCondition()
return cond.enforce(FCNN(3, 1), *x)
def vector_field(x):
cond = NoCondition()
return tuple(cond.enforce(FCNN(3, 1), *x) for _ in range(3))
def test_monitor_1d(history):
monitor = Monitor1D(0, 1)
nets = [FCNN() for _ in range(N_FUNCTIONS)]
conditions = [NoCondition() for _ in range(N_FUNCTIONS)]
monitor.check(nets, conditions, history=history)
def test_metrics_mointor(history):
monitor = MetricsMonitor(check_every=10)
nets = [FCNN(2, 1) for _ in range(N_FUNCTIONS)]
conditions = [NoCondition() for _ in range(N_FUNCTIONS)]
monitor.check(nets, conditions, history)