sigma_x and sigma_t in heat1D/heat1D.py

[smao-astro]

Hi,

In the line below

MultiscalePINNs/heat1D/heat1D.py

Lines 32 to 37 in f300c74

	def operator(u, t, x, k, sigma_t=1.0, sigma_x=1.0):
	u_t = tf.gradients(u, t)[0] / sigma_t
	u_x = tf.gradients(u, x)[0] / sigma_x
	u_xx = tf.gradients(u_x, x)[0] / sigma_x
	residual = u_t - k * u_xx
	return residual

I have two question:

1. Seems that when the function is called
   

   MultiscalePINNs/heat1D/models_tf.py

   Lines 600 to 604 in f300c74

   	def net_r(self, t, x):
   	u = self.net_u(t, x)
   	residual = self.operator(u, t, x, self.k,
   	self.sigma_t, self.sigma_x)
   	return residual

   
   you give slightly different sigma_x and sigma_t, does not that break the balance of the equation?
2. Why sigma_x occurred twice in the second term (spatial 2nd derivative)? Does this mean that you are actually changing the PDE you are solving?

In addition, I got an output below that seems different comparing with the figure 12 in the paper (using heat1D_ST_FF), do you have any idea?

[sifanexisted]

Hi,

We are happy to answer your questions.

A1: This is because we normalize the inputs and consequently changes the PDE we are solving. But if you do not normalize the input coordinates and take sigma_t = sigma_x = 1, then we believe you will get the similar results .

A2: This is because of the low resolution of the mesh grid used to visualize the results. If ou use a finer mesh, (e.g nn=1000), we believe the results you get should be similar to the results shown in our paper.

Let me know if you have any other questions.

[smao-astro]

So for the first question, that's because you are taking partial derivative w.r.t. the normalized input, and thus introduce an additional normalizing factor, to account for this, divide the partial derivative by sigma, I see.

For the second question, I changed nn to 1000, and used heat1D_ST_FF, by still can not reproduce the figure 12 in paper (see my output below), any idea?

Thanks.

[sifanexisted]

Then please use higher nn until you can reproduce the result.

…

On Sat, May 22, 2021 at 8:58 PM smao-astro ***@***.***> wrote: So for the first question, that's because you are taking partial derivative w.r.t. the normalized input, and thus introduce an additional normalizing factor, to account for this, divide the partial derivative by sigma, I see. For the second question, I changed nn to 1000, and used heat1D_ST_FF, by still can not reproduce the figure 12 in paper (see my output below), any idea? [image: heat1d_output-2] <https://user-images.githubusercontent.com/54871380/119244616-f4bd2800-bba4-11eb-8f85-76cf7fd8081d.png> Thanks. — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#2 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AQXONVOYGIYGKQXJADEH6XLTPBHNDANCNFSM45KN3EUA> .