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(x0, x1, y0, y1, ones, net11):
cond = DirichletBVP(x0, y0, x1, y1)
x = x0 * ones
y = cond.enforce(net11, x)
assert all_close(y, y0), "y(x_0) != y_0"
x = x1 * ones
y = cond.enforce(net11, x)
assert all_close(y, y1), "y(x_1) != y_1"
def test_dirichlet_bvp():
cond = DirichletBVP(x0, y0, x1, y1)
net = FCNN(1, 1)
x = x0 * ones
y = cond.enforce(net, x)
assert all_close(y, y0), "y(x_0) != y_0"
x = x1 * ones
y = cond.enforce(net, x)
assert all_close(y, y1), "y(x_1) != y_1"
def boundary_functions_2d(x0, x1, y0, y1, u00, u01, u10, u11):
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)
return f0, f1, g0, g1
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,
)