区域是正方形的扩散方程的边界该怎么设置？

[guanzongben]

您好，
扩散方程是：u_t = (D(x, y) * (u_xx + u_yy))
我想训练的算子是G：D→u
我在设置上下边界是1的时候程序运行的结果是图1。

但是为什么当我设置成四周都是1的时候结果是图2，这个结果和我用FEM计算的结果（图3）不太符合。

是我边界条件设置不对吗？麻烦帮我解答下，谢谢！以下是程序中边界条件的设置。

def pde(x, u, D_x):
du_t = dde.grad.jacobian(u, x, j=2)
du_xx = dde.grad.hessian(u, x, i=0, j=0)
du_yy = dde.grad.hessian(u, x, i=1, j=1)
return du_t - D_x * (du_xx + du_yy)

def on_boundary_condition_t(x, on_boundary):
return on_boundary and np.isclose(x[1], 1)
def on_boundary_condition_b(x, on_boundary):
return on_boundary and np.isclose(x[1], 0)
def on_boundary_condition_l(x, on_boundary):
return on_boundary and np.isclose(x[0], 0)
def on_boundary_condition_r(x, on_boundary):
return on_boundary and np.isclose(x[0], 1)
def boundary_condition_t_value(x):
return 1.
def boundary_condition_b_value(x):
return 1.
def boundary_condition_l_value(x):
return 1.
def boundary_condition_r_value(x):
return 1.
def initial_value(x):
return 0.
def on_initial_condition(x, on_initial):
return on_initial

geom = dde.geometry.Rectangle([0, 0], [1, 1])
timedomain = dde.geometry.TimeDomain(0, 1)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)

bc_t = dde.icbc.DirichletBC(geomtime, boundary_condition_t_value, on_boundary=on_boundary_condition_t, component=0)
bc_b = dde.icbc.DirichletBC(geomtime, boundary_condition_b_value, on_boundary=on_boundary_condition_b, component=0)

bc_b = dde.icbc.boundary_conditions.PeriodicBC(geomtime, component_x=1, on_boundary=on_boundary_condition_b)

bc_l = dde.icbc.DirichletBC(geomtime, boundary_condition_l_value, on_boundary=on_boundary_condition_l, component=0)
bc_r = dde.icbc.DirichletBC(geomtime, boundary_condition_r_value, on_boundary=on_boundary_condition_r, component=0)

bc_r = dde.icbc.boundary_conditions.PeriodicBC(geomtime, component_x=0, on_boundary=on_boundary_condition_r)

ic = dde.icbc.IC(geomtime, initial_value, on_initial_condition)

pde = dde.data.TimePDE(
geomtime,
pde,
[bc_t, bc_b,
bc_l, bc_r,
ic],
num_domain=1000,
num_boundary=600,
num_initial=600,
num_test=400,
)