boundary number error

[bmemlh]

Hello everyone,

I have an error related to number of boundary points for the problem. If the boundary number is increased until approximately 100000, no error emerges. However, when the boundary number is slightly increased from this point an error message pops out, as shown below:

_

ValueError Traceback (most recent call last)
Cell In[13], line 10
8 bc_C_n2 = dde.icbc.NeumannBC(geomtime, lambda x:0.0, boundary5)
9 ic_C = dde.icbc.IC(geomtime, lambda x:C0/C_scale, initial, component=0)
---> 10 data = dde.data.TimePDE(geomtime, pde, [bc_C_d1, bc_C_d2, bc_C_d3, bc_C_n1, bc_C_n2, ic_C], num_domain=300000, num_boundary=110000, num_test=100000, num_initial=100000)

File ~\anaconda3\lib\site-packages\deepxde\data\pde.py:322, in TimePDE.init(self, geometryxtime, pde, ic_bcs, num_domain, num_boundary, num_initial, train_distribution, anchors, exclusions, solution, num_test, auxiliary_var_function)
306 def init(
307 self,
308 geometryxtime,
(...)
319 auxiliary_var_function=None,
320 ):
321 self.num_initial = num_initial
--> 322 super().init(
323 geometryxtime,
324 pde,
325 ic_bcs,
326 num_domain,
327 num_boundary,
328 train_distribution=train_distribution,
329 anchors=anchors,
330 exclusions=exclusions,
331 solution=solution,
332 num_test=num_test,
333 auxiliary_var_function=auxiliary_var_function,
334 )

File ~\anaconda3\lib\site-packages\deepxde\data\pde.py:127, in PDE.init(self, geometry, pde, bcs, num_domain, num_boundary, train_distribution, anchors, exclusions, solution, num_test, auxiliary_var_function)
124 self.test_x, self.test_y = None, None
125 self.train_aux_vars, self.test_aux_vars = None, None
--> 127 self.train_next_batch()
128 self.test()

File ~\anaconda3\lib\site-packages\deepxde\utils\internal.py:38, in run_if_all_none..decorator..wrapper(self, *args, **kwargs)
36 x = [getattr(self, a) for a in attr]
37 if all(i is None for i in x):
---> 38 return func(self, *args, **kwargs)
39 return x if len(x) > 1 else x[0]

File ~\anaconda3\lib\site-packages\deepxde\data\pde.py:175, in PDE.train_next_batch(self, batch_size)
173 @run_if_all_none("train_x", "train_y", "train_aux_vars")
174 def train_next_batch(self, batch_size=None):
--> 175 self.train_x_all = self.train_points()
176 self.bc_points() # Generate self.num_bcs and self.train_x_bc
177 if self.bcs and config.hvd is not None:

File ~\anaconda3\lib\site-packages\deepxde\utils\internal.py:38, in run_if_all_none..decorator..wrapper(self, *args, **kwargs)
36 x = [getattr(self, a) for a in attr]
37 if all(i is None for i in x):
---> 38 return func(self, *args, **kwargs)
39 return x if len(x) > 1 else x[0]

File ~\anaconda3\lib\site-packages\deepxde\data\pde.py:338, in TimePDE.train_points(self)
336 @run_if_all_none("train_x_all")
337 def train_points(self):
--> 338 X = super().train_points()
339 if self.num_initial > 0:
340 if self.train_distribution == "uniform":

File ~\anaconda3\lib\site-packages\deepxde\utils\internal.py:38, in run_if_all_none..decorator..wrapper(self, *args, **kwargs)
36 x = [getattr(self, a) for a in attr]
37 if all(i is None for i in x):
---> 38 return func(self, *args, **kwargs)
39 return x if len(x) > 1 else x[0]

File ~\anaconda3\lib\site-packages\deepxde\data\pde.py:265, in PDE.train_points(self)
263 tmp = self.geom.uniform_boundary_points(self.num_boundary)
264 else:
--> 265 tmp = self.geom.random_boundary_points(
266 self.num_boundary, random=self.train_distribution
267 )
268 X = np.vstack((tmp, X))
269 if self.anchors is not None:

File ~\anaconda3\lib\site-packages\deepxde\geometry\timedomain.py:147, in GeometryXTime.random_boundary_points(self, n, random)
145 t = self.timedomain.random_points(n, random=random)
146 t = np.random.permutation(t)
--> 147 return np.hstack((x, t))

File <array_function internals>:180, in hstack(*args, **kwargs)

File ~\anaconda3\lib\site-packages\numpy\core\shape_base.py:345, in hstack(tup)
343 return _nx.concatenate(arrs, 0)
344 else:
--> 345 return _nx.concatenate(arrs, 1)

File <array_function internals>:180, in concatenate(*args, **kwargs)

ValueError: all the input array dimensions for the concatenation axis must match exactly, but along dimension 0, the array at index 0 has size 109999 and the array at index 1 has size 110000

_

In addition, when I assign the number of boundary points as 300000, the inconsistency between the matrices are varied as below:

ValueError: all the input array dimensions for the concatenation axis must match exactly, but along dimension 0, the array at index 0 has size 299997 and the array at index 1 has size 300000

I don't have any idea why is this happening, please help me
Thank you!

[lululxvi]

It is strange. Could you show a minimal code example to reproduce the error?

[bmemlh]

Thank you for your interest Lu Lu!

Here is the relevant part of my code:

``
geom = dde.geometry.Rectangle(xmin=[0, 0], xmax=[10, 40])
timedomain = dde.geometry.TimeDomain(0, 2)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)
bc_C_d1 = dde.icbc.PointSetBC(coordinate_time_points, concentration_values, component=0)
bc_C_d2 = dde.icbc.DirichletBC(geomtime, lambda x:C0/C_scale, boundary1)
bc_C_d3 = dde.icbc.DirichletBC(geomtime, lambda x:C0/C_scale, boundary2)
bc_C_n1 = dde.icbc.NeumannBC(geomtime, lambda x:0.0, boundary3)
bc_C_n2 = dde.icbc.NeumannBC(geomtime, lambda x:0.0, boundary4)
ic_C = dde.icbc.IC(geomtime, lambda x:C0/C_scale, initial, component=0)
data = dde.data.TimePDE(geomtime, pde, [bc_C_d1, bc_C_d2, bc_C_d3, bc_C_n1, bc_C_n2, ic_C], num_domain=300000, num_boundary=120000, num_test=100000, num_initial=100000)
`
Solver runs perfectly when the num_boundary is lower than or equal to 100000 but when it increases to approximately 101000 the aforementioned error message emerges

Thanks again!

[lululxvi]

Could you send a complete but simple code so I can run and reproduce the error?

[bmemlh]

Thank you for your interest Lu Lu,

Here is the full code:

import deepxde as dde
import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf
import sys

R = 8.3145
Temp = 300.0
F = 96485.0
Ei = 0.5
Es = -0.5
Vs = 0.001
k0 = 0.050119
C0 = 1.0
L = 0.001
D = 1e-9
timemax = 2000.0
L_scale = L
D_scale = D
C_scale = C0
E_scale = (R*Temp)/F
Vs_scale = Vs
t_scale = (L*L)/D

def pde(x, C):
    dC_x = dde.grad.jacobian(C, x, j=0)
    dC_t = dde.grad.jacobian(C, x, j=2)
    dC_xx = dde.grad.hessian(C, x, i=0, j=0)
    dC_yy = dde.grad.hessian(C, x, i=1, j=1)
    NP = dC_t - (dC_xx+dC_yy)
    return NP

def boundary1(x, _):
    return np.isclose(x[0], 10)

def boundary2(x, _):
    return np.isclose(x[1], 40)

def boundary3(x, _):
    return np.greater_equal(x[0], 1) and np.less_equal(x[0], 10) and np.equal(x[1], 0)

def boundary4(x, _):
    return np.isclose(x[0], 0)

def initial(_, on_initial):
    return on_initial

time_points = np.array([])
a = np.array([0.0])
for i in range(1001):
    for j in range(201):
        time_points = np.append(time_points, a, axis=0)
    a = a + 0.002
time_points = time_points.reshape(time_points.shape[0], 1)

coordinate_points_x = np.array([])
for k in range(1001):
    coordinate_points_x = np.append(coordinate_points_x, np.arange(0, 1.005, 0.005), axis=0)
coordinate_points_y = np.repeat(0, 1001*201)
coordinate_points_x = coordinate_points_x.reshape(coordinate_points_x.shape[0], 1)
coordinate_points_y = coordinate_points_y.reshape(coordinate_points_y.shape[0], 1)
coordinate_time_points = np.concatenate([coordinate_points_x, coordinate_points_y, time_points], axis=1)

E1 = Ei/E_scale - ((Vs*t_scale)/E_scale)*time_points[0:100601]
E2 = Es/E_scale + ((Vs*t_scale)/E_scale)*(time_points[100601:201201]-(timemax/(2*t_scale)))
concentration1 = 1.0/(1.0+np.exp(-E_scale*(F/(R*Temp))*E1))
concentration2 = 1.0/(1.0+np.exp(-E_scale*(F/(R*Temp))*E2))
concentration_values = np.concatenate([concentration1, concentration2], axis=0)
concentration_values = concentration_values.reshape(concentration_values.shape[0], 1)

geom = dde.geometry.Rectangle(xmin=[0, 0], xmax=[10, 40])
timedomain = dde.geometry.TimeDomain(0, 2)
geomtime = dde.geometry.GeometryXTime(geom, timedomain)
bc_C_d1 = dde.icbc.PointSetBC(coordinate_time_points, concentration_values, component=0)
bc_C_d2 = dde.icbc.DirichletBC(geomtime, lambda x:C0/C_scale, boundary1)
bc_C_d3 = dde.icbc.DirichletBC(geomtime, lambda x:C0/C_scale, boundary2)
bc_C_n1 = dde.icbc.NeumannBC(geomtime, lambda x:0.0, boundary3)
bc_C_n2 = dde.icbc.NeumannBC(geomtime, lambda x:0.0, boundary4)
ic_C = dde.icbc.IC(geomtime, lambda x:C0/C_scale, initial, component=0)
data = dde.data.TimePDE(geomtime, pde, [bc_C_d1, bc_C_d2, bc_C_d3, bc_C_n1, bc_C_n2, ic_C], num_domain=300000, num_boundary=150000, num_test=200000, num_initial=200000)

layer_size = [3]+[30]*3+[1]
activation = "tanh"
initializer = "Glorot normal"
net = dde.nn.FNN(layer_size, activation, initializer)
model = dde.Model(data, net)

resampler = dde.callbacks.PDEPointResampler(period=50)
model.compile("adam", lr=5e-4)
losshistory, train_state = model.train(iterations=20000, callbacks=[resampler])
dde.saveplot(losshistory, train_state, issave=False, isplot=True)

Thanks a lot again!