Can deepxde be dimensionless?

[staarr]

Hi @lululxvi , In some special cases, the input and output need to be scaled to a certain range. Take the following example: def pde(x,y): c_star=4.0 r_star=20.0 t_star=30.0 yd = y/c_star rd = x[:,0]/r_star td = x[:,1]/t_star dy_t = dde.grad.jacobian(yd,td,i=0,j=0) dy_rr = dde.grad.hessian(yd,rd,i=0,j=0) return dy_rr-dy_t But there will be an error running, how to solve it?

[jdellag]

FWIW, I never have division anywhere inside my PDE function. In the past it has resulted in nan values in my losses and just created a lot of numerical instability. Was it a hassle to reformulate everything in order to handle this? Yes, but it was the only thing to make the program run.

[haison19952013]

Let's use some mathematics to overcome this problem. For example, you can use the chain rule to compute dy'/dt' as followings:

• dy'/dt' = dy'/dy dy/dt dt / dt'
  where
• dy'/dy = 1/c_star because y' = y/c_start
• dt / dt' = t_star because t' = t/t_start

So the final code should be: dy_prime_dt_prime = dde.grad.jacobian(y,t,i=0,j=0) * t_star/c_star