Ground truth generated for the reaction diffusion equation and reaction equation

[arkadaw9]

The ground truth (exact) data generated for the reaction diffusion equation with $\rho=5$ and $\nu=5$ using the code is different from that of the paper.

Here is the ground truth shown in the paper:

Here is the one I get from the code:

The same happens for the reaction equation as well. Could you please help me figure out if its the problem of the ground-truth generation or I'm doing something wrong?

Thanks,
Arka

[winnie-chu-aos]

Hello,

This is late but I encountered the same problem as well. I resolved it by changing the argument for initial conditions "u0_str" to "gauss" instead of the default "sin(x)".

We make this change because in the paper, the authors use the initial condition u(x,0) = $\exp(-\frac{(x-\pi)^2}{2(\pi/4)^2})$ (Eq. 17) to solve the reaction equation. (If you go into the systems.py file, you can see that the "gauss" option for "u0_str" is the same equation.) When we solve the reaction-diffusion equation, we solve the reaction equation internally, so this initial condition should be the same.

For $\rho = 5$ and $\nu = 5$, the ground truth is

and the PINN prediction is

Hope this helps someone in the future!