How to set up different materials in the electrical field?

[Blackrobin15]

Hello, Lu Lu
I am trying to set up different materials in the electrical field. But I have no idea how to set the permittivity in different regions. Could you please give me some advice?
Thanks a lot

def perm(x):
    if geom_cir.inside(x):
        return 6
    else:
        return 1
    
def pde(x,u):
    du_x = dde.grad.jacobian(u, x, i=0, j=0)
    du_y = dde.grad.jacobian(u, x, i=0, j=1)
    #du_xx=geom_cir.inside(x)*1*dde.grad.jacobian(du_x, x, i=0, j=0)+(~geom_cir.inside(x)*4*dde.grad.jacobian(du_x, x, i=0, j=0))
    #du_yy=geom_cir.inside(x)*1*dde.grad.jacobian(du_y, x, i=0, j=1)+(~geom_cir.inside(x)*4*dde.grad.jacobian(du_y, x, i=0, j=1))
    #du_xx=perm(x)*dde.grad.jacobian(du_x, x, i=0, j=0)
    du_xx=np.heaviside(x[:,0:1],1)*dde.grad.jacobian(du_x, x, i=0, j=0)
    du_yy=np.heaviside(x[:,1:2],1)*dde.grad.jacobian(du_x, x, i=0, j=1)
    return du_xx+du_yy
    

NotImplementedError: Cannot convert a symbolic Tensor (strided_slice_2:0) to a numpy array. This error may indicate that you're trying to pass a Tensor to a NumPy call, which is not supported

The error occurred in the code:
model.compile("adam", lr=1.0e-3)

The details are as follows ：

NotImplementedError Traceback (most recent call last)
in
2 model = dde.Model(data, net)
3
----> 4 model.compile("adam", lr=1.0e-3)
5 #model.train(epochs=10000)
6 #model.compile("L-BFGS")

D:\Anaconda3\lib\site-packages\deepxde\utils\internal.py in wrapper(*args, **kwargs)
20 def wrapper(*args, **kwargs):
21 ts = timeit.default_timer()
---> 22 result = f(*args, **kwargs)
23 te = timeit.default_timer()
24 print("%r took %f s\n" % (f.name, te - ts))

D:\Anaconda3\lib\site-packages\deepxde\model.py in compile(self, optimizer, lr, loss, metrics, decay, loss_weights, external_trainable_variables)
105
106 if backend_name == "tensorflow.compat.v1":
--> 107 self._compile_tensorflow_compat_v1(lr, loss_fn, decay, loss_weights)
108 elif backend_name == "tensorflow":
109 self._compile_tensorflow(lr, loss_fn, decay, loss_weights)

D:\Anaconda3\lib\site-packages\deepxde\model.py in _compile_tensorflow_compat_v1(self, lr, loss_fn, decay, loss_weights)
125
126 # Data losses
--> 127 losses = self.data.losses(self.net.targets, self.net.outputs, loss_fn, self)
128 if not isinstance(losses, list):
129 losses = [losses]

D:\Anaconda3\lib\site-packages\deepxde\data\pde.py in losses(self, targets, outputs, loss, model)
127 if self.pde is not None:
128 if get_num_args(self.pde) == 2:
--> 129 f = self.pde(model.net.inputs, outputs)
130 elif get_num_args(self.pde) == 3:
131 if self.auxiliary_var_fn is None:

in pde(x, u)
11 #du_yy=geom_cir.inside(x)1dde.grad.jacobian(du_y, x, i=0, j=1)+(~geom_cir.inside(x)4dde.grad.jacobian(du_y, x, i=0, j=1))
12 #du_xx=perm(x)*dde.grad.jacobian(du_x, x, i=0, j=0)
---> 13 du_xx=np.heaviside(x[:,:1],1)*dde.grad.jacobian(du_x, x, i=0, j=0)
14 #return du_xx+du_yy
15 return du_xx

D:\Anaconda3\lib\site-packages\tensorflow\python\framework\ops.py in array(failed resolving arguments)
918 def array(self, dtype=None):
919 del dtype
--> 920 raise NotImplementedError(
921 "Cannot convert a symbolic Tensor ({}) to a numpy array."
922 " This error may indicate that you're trying to pass a Tensor to"

NotImplementedError: Cannot convert a symbolic Tensor (strided_slice_2:0) to a numpy array. This error may indicate that you're trying to pass a Tensor to a NumPy call, which is not supported

[lululxvi]

Use auxiliary_var_function, see example https://github.com/lululxvi/deepxde/blob/master/examples/Lorenz_inverse_forced.ipynb

[Blackrobin15]

Thanks for your reply!
I've read your comments #79 (comment)
I think the reason may be that x in pde(x,u) is using tensorflow, but geometry.inside(x) function is using numpy. I am trying to using tf.where() to solve this problem. It seems like that I need to define the geometric areas of different materials in pde(x,u).

[Blackrobin15]

Hello, Dr. Lu @lululxvi
It seems like I have solve different materials setting problem with tf.where(). But I found that the pde() function did not work as as expected. The physical scenario is as follows:

My pde function setting is:

def pde(x,u):
    du_x = dde.grad.jacobian(u, x, i=0, j=0)
    du_y = dde.grad.jacobian(u, x, i=0, j=1)
    #the center of the circle (1,1), radius 0.5 
    condition=tf.less((x[:,0:1]-1.0)**2+(x[:,1:2]-1.0)**2,0.25)
    pe=tf.where(condition,4.0,1.0)
    result=dde.grad.jacobian(pe*du_x, x, i=0, j=0)+dde.grad.jacobian(pe*du_x, x, i=0, j=1)
    return result

What might be the problem with this representation?

[lululxvi]

The code looks OK. What doesn't work as expected?

[Blackrobin15]

Thank you for your reply! I use a FEM work for comparison, The FEM result is as follow:

The DeepXDE result is as follow:

It seems like the change happens into y in [1.75,2] not in the circle area. This confuses me.

[lululxvi]

Instead of tf.where, could you try auxiliary_var_function?

[Blackrobin15]

Thanks for your help!
I am going to try to code with auxiliary_var_function right now and I uploaded my datas and codes in https://github.com/Blackrobin15/Questions in folder Question1.
If you have time, could you please take a look?

[aminetazarine]

Use auxiliary_var_function, see example https://github.com/lululxvi/deepxde/blob/master/examples/Lorenz_inverse_forced.ipynb

Hello lululxvi
Can you please send the code for this function (auxiliary_var_function) because this link does not work.
Another question: can we use np.where instead of tf.where.
One more
Thank you.

[lululxvi]

You can find the examples at https://deepxde.readthedocs.io/en/latest/demos/pinn_inverse.html

Use np.where for numpy array; use tf.where for tensor.

[aminetazarine]

Hello Lululxvi
Please i need your help how can i use auxiliary_var_function Instead of tf.where, because i want to set the permittivity in different regions this is my pde:
def pde(x, y):

ep*dEz/dt -dHy/dx+dHx/dy=0

Ez, Hx, Hy = y[:, 0:1], y[:, 1:2], y[:, 2:3]
dEz_x = dde.grad.jacobian(y, x, i=0, j=0) #dEz/dx
dEz_y = dde.grad.jacobian(y, x, i=0, j=1) #dEz/dy
dEz_t = dde.grad.jacobian(y, x, i=0, j=2) #dEz/dt


dHx_x = dde.grad.jacobian(y, x, i=1, j=0) #dHx/dx
dHx_y = dde.grad.jacobian(y, x, i=1, j=1) #dHx/dy
dHx_t = dde.grad.jacobian(y, x, i=1, j=2) #dHx/dt

dHy_x = dde.grad.jacobian(y, x, i=2, j=0) #dHy/dx
dHy_y = dde.grad.jacobian(y, x, i=2, j=1) #dHy/dy
dHy_t = dde.grad.jacobian(y, x, i=2, j=2) #dHy/dt

#this is the condtion of ep ===> ep=2 if 0<=x<=0.5 and ep=1 if 0.5<=x<=1

cond=tf.less(x[:,0:1],0.5)
epsilon_1=dde.Variable(1.0)
epsilon_2=dde.Variable(2.0)
f1 =epsilon_2*dEz_t-dHy_x+dHx_y 
f2 =epsilon_1*dEz_t-dHy_x+dHx_y 
f=tf.where(cond,f1,f2)
return f

It is true?/??

[lululxvi]

epsilon_1 = 1
epsilon_2 = 2

[chang-change]

@lululxvi
Hello Lulu,
I use auxiliary_var_function Instead of tf.where, but I don't know if it's right?
This is my code:

def epsilon(x):
    #the center of the circle (1,1), radius 0.5
    if (x[:,0:1]-1)**2 + (x[:,1:2]-1)**2 <0.25:
        ep = 4
    else:
        ep = 1
    return ep 


def pde(x,u,ex):
    du_x = dde.grad.jacobian(u, x, i=0, j=0)
    du_y = dde.grad.jacobian(u, x, i=0, j=1)
     

    result=dde.grad.jacobian(epsilon*du_x, x, i=0, j=0)+dde.grad.jacobian(epsilon*du_x, x, i=0, j=1)
    return result

data = dde.data.PDE(
    geom,
    pde,
    [bc],
    num_domain=400,
    num_boundary=2,
    auxiliary_var_function=epsilon,
)

Thank you.

[lululxvi]

Looks good.

[ach14012022]

@chang-change Please let me know if your code is run without any error.

[chang-change]

@ach14012022 I don't have the complete code, I just modified this piece of code. Hence, I don't know if it will work successfully.

[mengxia123]

感谢您的帮助！我现在要尝试编码，我将我的数据和代码上传到 https://github.com/Blackrobin15/Questions 文件夹中的问题 1。如果你有时间，可以看看吗？auxiliary_var_function

感谢您的帮助！我现在要尝试编码，我将我的数据和代码上传到 https://github.com/Blackrobin15/Questions 文件夹中的问题 1。如果你有时间，可以看看吗？auxiliary_var_function
您好，同学。我最近也在做电气领域不同介质的PDE，遇到的问题和你一样，能否借鉴下你的代码，是怎么处理。万分感谢

[Blackrobin15]

In fact, I used a little trick that I saw in a paper 10.1021/acsphotonics.0c01202. You can read it if you are interested. Another method is to use tf.where as the corresponding dielectric constant for residual points in different positions as mentioned above.

感谢您的帮助！我现在要尝试编码，我将我的数据和代码上传到 https://github.com/Blackrobin15/Questions 文件夹中的问题 1。如果你有时间，可以看看吗？auxiliary_var_function

感谢您的帮助！我现在要尝试编码，我将我的数据和代码上传到 https://github.com/Blackrobin15/Questions 文件夹中的问题 1。如果你有时间，可以看看吗？auxiliary_var_function
您好，同学。我最近也在做电气领域不同介质的PDE，遇到的问题和你一样，能否借鉴下你的代码，是怎么处理。万分感谢

[mengxia123]

Thank you for your reply! I use a FEM work for comparison, The FEM result is as follow:

The DeepXDE result is as follow:

It seems like the change happens into y in [1.75,2] not in the circle area. This confuses me.

I'm not sure if your problem has been solved? I am currently working in this direction and need to be confused, such as how to handle the same domain, different PDEs, interfaces, etc. Could you please refer to your code for me to learn. obliged to sb.