understanding the EquationClass from ShockRarEntropy.py

[reyhashemi]

Hi Roberto and thank you for sharing the WPINN paper's code with us.

I read the paper and went through the repository. I have some doubts with respect to some details in the code which I would like to check with you. I would be grateful if you could provide me with some clarifying elements.

1- In phi = w * theta ** 2 why is teta powered to 2 while in the paper (Page 11, line 16) it is not?

2- could you please elaborate a bit on how and why you define c from u0. I am referring to these code lines in particular:

min_c = 2 * torch.min(self.u0(torch.linspace(-1, 1, 1000)))
max_c = 2 * torch.max(self.u0(torch.linspace(-1, 1, 1000)))

3- could you please provide some references regarding the definition of the different cutoff functions you define via def fun_w(self, x, extrema_values, time_dimensions) and the "partial weakness" equation you used.

4- Just to make sure that I am not misunderstanding, could you please precise what are the following variables:

• c_mode ? (when you define 'self.c_mode = "max" ')
• extrema_values
• ubx0, ubx1, u0

5- could you please confirm that the reason for which you use torch.mean and not torch.sum in the definition of the norms (L2, H1, ..) is because you wish to rely on a relative norm ?

Thank you in advance for your time.