def test_ivp(x0, y0, y1, ones, net11):
x = x0 * ones
cond = IVP(x0, y0)
y = cond.enforce(net11, x)
assert torch.isclose(y, y0 * ones).all(), "y(x_0) != y_0"
cond = IVP(x0, y0, y1)
y = cond.enforce(net11, x)
assert all_close(y, y0), "y(x_0) != y_0"
assert all_close(diff(y, x), y1), "y'(x_0) != y'_0"
def test_ivp():
x = x0 * ones
net = FCNN(1, 1)
cond = IVP(x0, y0)
y = cond.enforce(net, x)
assert torch.isclose(y, y0 * ones).all(), "y(x_0) != y_0"
cond = IVP(x0, y0, y1)
y = cond.enforce(net, x)
assert all_close(y, y0), "y(x_0) != y_0"
assert all_close(diff(y, x), y1), "y'(x_0) != y'_0"
def test_ibvp_1d():
t0, t1 = random.random(), random.random()
u00, u01, u10, u11 = [random.random() for _ in range(4)]
# set the initial condition ut0(x) = u(x, t0)
net_ut0 = FCNN(1, 1)
cond_ut0 = DirichletBVP(x0, u00, x1, u10)
ut0 = lambda x: cond_ut0.enforce(net_ut0, x)
# set the Dirichlet boundary conditions g(t) = u(x0, t) and h(t) = u(x1, t)
net_g, net_h = FCNN(1, 1), FCNN(1, 1)
cond_g = IVP(t0, u00)
cond_h = IVP(t0, u10)
g = lambda t: cond_g.enforce(net_g, t)
h = lambda t: cond_h.enforce(net_h, t)
# set the Neumann boundary conditions p(t) = u'_x(x0, t) and q(t) = u'_x(x1, t)
x = x0 * ones
p0 = diff(ut0(x), x)[0, 0].item()
x = x1 * ones
q0 = diff(ut0(x), x)[0, 0].item()
p1, q1 = random.random(), random.random()
net_p, net_q = FCNN(1, 1), FCNN(1, 1)
cond_p = DirichletBVP(t0, p0, t1, p1)
cond_q = DirichletBVP(t0, q0, t1, q1)
p = lambda t: cond_p.enforce(net_p, t)
q = lambda t: cond_q.enforce(net_q, t)
# initialize a random network
net = FCNN(2, 1)
# test Dirichlet-Dirichlet condition
condition = IBVP1D(x0, x1, t0, ut0, x_min_val=g, x_max_val=h)
x = torch.linspace(x0, x1, N_SAMPLES, requires_grad=True).view(-1, 1)
t = t0 * ones
assert all_close(condition.enforce(net, x, t),
ut0(x)), "initial condition not satisfied"
x = x0 * ones
t = torch.linspace(t0, t1, N_SAMPLES, requires_grad=True).view(-1, 1)
assert all_close(condition.enforce(net, x, t),
g(t)), "left Dirichlet BC not satisfied"
x = x1 * ones
t = torch.linspace(t0, t1, N_SAMPLES, requires_grad=True).view(-1, 1)
assert all_close(condition.enforce(net, x, t),
h(t)), "right Dirichlet BC not satisfied"
# test Dirichlet-Neumann condition
condition = IBVP1D(x0, x1, t0, ut0, x_min_val=g, x_max_prime=q)
x = torch.linspace(x0, x1, N_SAMPLES, requires_grad=True).view(-1, 1)
t = t0 * ones
assert all_close(condition.enforce(net, x, t),
ut0(x)), "initial condition not satisfied"
x = x0 * ones
t = torch.linspace(t0, t1, N_SAMPLES, requires_grad=True).view(-1, 1)
assert all_close(condition.enforce(net, x, t),
g(t)), "left Dirichlet BC not satisfied"
x = x1 * ones
t = torch.linspace(t0, t1, N_SAMPLES, requires_grad=True).view(-1, 1)
assert all_close(diff(condition.enforce(net, x, t), x),
q(t)), "right Neumann BC not satisfied"
# test Neumann-Dirichlet condition
condition = IBVP1D(x0, x1, t0, ut0, x_min_prime=p, x_max_val=h)
x = torch.linspace(x0, x1, N_SAMPLES, requires_grad=True).view(-1, 1)
t = t0 * ones
assert all_close(condition.enforce(net, x, t),
ut0(x)), "initial condition not satisfied"
x = x0 * ones
t = torch.linspace(t0, t1, N_SAMPLES, requires_grad=True).view(-1, 1)
assert all_close(diff(condition.enforce(net, x, t), x),
p(t)), "left Neumann BC not satisfied"
x = x1 * ones
t = torch.linspace(t0, t1, N_SAMPLES, requires_grad=True).view(-1, 1)
assert all_close(condition.enforce(net, x, t),
h(t)), "right Dirichlet BC not satisfied"
# test Neumann-Neumann condition
condition = IBVP1D(x0, x1, t0, ut0, x_min_prime=p, x_max_prime=q)
x = torch.linspace(x0, x1, N_SAMPLES, requires_grad=True).view(-1, 1)
t = t0 * ones
assert all_close(condition.enforce(net, x, t),
ut0(x)), "initial condition not satisfied"
x = x0 * ones
t = torch.linspace(t0, t1, N_SAMPLES, requires_grad=True).view(-1, 1)
assert all_close(diff(condition.enforce(net, x, t), x),
p(t)), "left Neumann BC not satisfied"
x = x1 * ones
t = torch.linspace(t0, t1, N_SAMPLES, requires_grad=True).view(-1, 1)
assert all_close(diff(condition.enforce(net, x, t), x),
q(t)), "right Neumann BC not satisfied"
# test unimplemented combination of conditions
with raises(NotImplementedError):
IBVP1D(
t_min=0,
t_min_val=lambda x: 0,
x_min=0,
x_min_val=None,
x_min_prime=None,
x_max=1,
x_max_val=None,
x_max_prime=None,
)
with raises(NotImplementedError):
IBVP1D(
t_min=0,
t_min_val=lambda x: 0,
x_min=0,
x_min_val=lambda t: 0,
x_min_prime=lambda t: 0,
x_max=1,
x_max_val=None,
x_max_prime=None,
)
with raises(NotImplementedError):
IBVP1D(
t_min=0,
t_min_val=lambda x: 0,
x_min=0,
x_min_val=None,
x_min_prime=lambda t: 0,
x_max=1,
x_max_val=None,
x_max_prime=None,
)