A question of the derivatives

[nlqnly]

Thanks for sharing the codes of the PDE-based PINN. However, I cannot understand why the derivatives need to multiply and divide the model size, like in the code for first order derivatives: du_y, dv_x = du_ya/b, dv_xb/a, and for second order derivatives: du_xx, du_yy, du_xy = du_xx/a, du_yy*a/b**2, du_xy/b. We're guessing that these are modifications for implicit derivatives. We sincerely invite your guidance, thank you!

[weili101]

Thanks for your interest in this work. Those modifications are for the purpose of rescaling the input coordinates within [0, 1] or [-1, 1]. Suppose that the true coordinates x', y' are in the range [0, a] and [0, b], the actual input coordinates will be x=x'/a and y=y'/b within range [0, 1]. The same was done for the outputs u=u'/a and v=v'/b (this is actually not necessary). Therefore, we will have the true derivative du'/dy' = du/dy*a/b.
Hope that helps!

[nlqnly]

Thanks for your answer! We have understood it.