BC Over a Right Angle Triangle

[sumantkrsoni]

Dear @lululxvi

I have defined a right angle triangle using the geometry code as:

geom = dde.geometry.Triangle([0,0], [1,0], [0,1])

Now, I am trying to implement a BC over the inclined edge of the triangle. For that I have written as:

    def func(x):
            return np.zeros((len(x), 1))

    def func_1(x):
            return np.ones((len(x), 1) )


    def boundary_l(x, on_boundary):
            return on_boundary and np.isclose(x[0], 0)

    def boundary_lwr(x, on_boundary):
            return on_boundary and np.isclose(x[1], 1)

    def boundary_incline(x, on_boundary):
            return on_boundary and np.isclose(x[1], 1- x[0])

My doubt is for boundary_incline
is it ok according to the problem definition.

Kindly, suggest.

[lululxvi]

Looks good.

[sumantkrsoni]

Thanks @lululxvi
unfortunately, it shows some error for not implementation on geometry type.

  File "D:/deepxde-master/deepxde-master\deepxde\geometry\geometry.py", line 23, in on_boundary
    raise NotImplementedError("{}.on_boundary to be implemented".format(self.idstr))
NotImplementedError: Triangle.on_boundary to be implemented

It seems on_boundary for the module has not been implemented.

I have attached the code here. Kindly Suggest me.

triangle.zip

[lululxvi]

I have implemented them. You can download the updated code.

[sumantkrsoni]

Thanks @lululxvi
It works, now I am trying to validate the result with it.

[sumantkrsoni]

Dear @lululxvi
I have implemented the code for natural convection over the triangle but the DeepXDE result is not showing according to the computed result from other platforms( using the FEM method).

FYI: triangle geometry has been chosen with parameters:
Ra = 100, AspectRation(AR) = 0.5

for that, the result for streamline and isotherm contours should be like:

but the deep learning method shows the result below which is not the same from the above result:

I am confused about it, that where I am going wrong.

the attachment includes code for it.

triangle.zip

It would be helpful for me if I could get a Suggestion regarding it.

Thanks.

[lululxvi]

You may check "Q: I failed to train the network or get the right solution, e.g., the training loss is large." at FAQ first.

[sumantkrsoni]

Thanks @lululxvi
After increasing the no of epochs the result has improved up to some extent but still, some modifications needed. Fo that I have enforced the BC after taking the reference from FAQ.

for implementing the BC:
over right angle triangle:

S = 0 on all sides of the triangular domain.

T = 1 on y=0
T = 0 on inclined side. i.e y = 1-x

New parameters are as imposed as:

S_new = x * y * ( 1-x - y) * S

T_new = (1-x-y)* (1-y)* T

and its code is:

    net.apply_output_transform(  lambda x, y : tf.concat([
                                                        x[:,0:1]*x[:, 1:2]*(1-x[:, 0:1]-x[:, 1:2])*y[:,0:1],
                                                         (1 - x[:.0:1] - x[:,1:2])* (1-x[:,1:2]) * y[:, 1:2]
                                                         ], axis = 1 )  )

but, unfortunately I am getting an error:

Traceback (most recent call last):
  File "D:\DIAT_PhD\PhD_Content\Coding_Script\TrianglePorous\triangle.py", line 104, in <module>
    main()
  File "D:\DIAT_PhD\PhD_Content\Coding_Script\TrianglePorous\triangle.py", line 89, in main
    model.compile("adam", lr=0.002)
  File "D:/deepxde-master/deepxde-master\deepxde\utils.py", line 52, in wrapper
    result = f(*args, **kwargs)
  File "D:/deepxde-master/deepxde-master\deepxde\model.py", line 76, in compile
    self.net.build()
  File "D:/deepxde-master/deepxde-master\deepxde\utils.py", line 52, in wrapper
    result = f(*args, **kwargs)
  File "D:/deepxde-master/deepxde-master\deepxde\maps\fnn.py", line 70, in build
    self.y = self._output_transform(self.x, self.y)
  File "D:\DIAT_PhD\PhD_Content\Coding_Script\TrianglePorous\triangle.py", line 85, in <lambda>
    (1 - x[:.0:1] - x[:,1:2])* (1-x[:,1:2]) * y[:, 1:2] ], axis = 1 )  )
  File "C:\Users\SUMANT\AppData\Local\Programs\Python\Python37\lib\site-packages\tensorflow_core\python\ops\array_ops.py", line 841, in _slice_helper
    _check_index(s.stop)
  File "C:\Users\SUMANT\AppData\Local\Programs\Python\Python37\lib\site-packages\tensorflow_core\python\ops\array_ops.py", line 752, in _check_index
    raise TypeError(_SLICE_TYPE_ERROR + ", got {!r}".format(idx))
TypeError: Only integers, slices (`:`), ellipsis (`...`), tf.newaxis (`None`) and scalar tf.int32/tf.int64 tensors are valid indices, got 0.0

Please suggest me.

[lululxvi]

Why the dot in x[:.0:1]?

[sumantkrsoni]

Why the dot in x[:.0:1]?

sorry for typo error and Thanks @lululxvi
Now It's working.

[sumantkrsoni]

Dear @lululxvi Sir,
The above problem, I have been trying to solve but I am getting a huge training loss without enforcing exact BC.

Under the following criteria:

• Rayleigh No: 100

Ra = 100.0

• PDE definition

        S, T = y[:,0:1], y[:, 1:2]
        dS_x = tf.gradients(S,x)[0]
        dT_x = tf.gradients(T,x)[0]

        dS_x, dS_y= dS_x[:,0:1], dS_x[:,1:2]
        dT_x, dT_y = dT_x[:,0:1], dT_x[:,1:2]

        dS_xx = tf.gradients(dS_x, x )[0][:,0:1]
        dS_yy = tf.gradients(dS_y, x )[0][:,1:2]

        dT_xx = tf.gradients(dT_x, x)[0][:, 0:1]
        dT_yy = tf.gradients(dT_y, x)[0][:, 1:2]


        return[ dS_xx + dS_yy + Ra * dT_x,
                dS_y*dT_x - dS_x*dT_y - dT_xx - dT_yy]

• Data Definition

data = dde.data.PDE(geom, pde, [..........], num_domain = 8000, num_boundary = 5000, num_test = 10000)

• Layer size and other parameters:

`
layer_size = [2] + [250]*3 + [2]
......................
model.compile("adam", lr=0.0001)
......................
losshistory, train_state = model.train(epochs = 10000, .............)

`

for cross-validating the training process I have compiled only for 10K iteration to see the training loss progress but no luck here, I have found.

training loss is:

The similar scenario are occuring in #84 ,
If I could get any idea about dealing such issue, that would be helpful for me.

kindly comment something.

Thanks in advance

Attched File for code script is:
triangle_2a.zip

[sumantkrsoni]

Dear @lululxvi Sir,

If I am not wrong, DeepXDE is based on the PINN approach.

Sir, do you have any example coded over the Penalty approach over the Feedforward neural network?

I have coded few problems over DeepXDE and want to see the comparison by the Penalty approach.

I have coded in DeepXDE for the simple first-order problem and now I am interested in solving it with a penalty approach.

I have coded it but not getting the exact solution.

• I am stuck with the training of the data over the boundary of the domain.

If possible, suggest me, please.

first_order.zip

[lululxvi]

What do you mean exactly by "Penalty approach"?