Difficulty in Setting Initial Conditions

[davidsohutskay]

Hello,

I have been trying to write a code to solve a reaction-diffusion type problem. I wanted to compare deepXDE and SciANN but was having difficulty getting my initial conditions set up in SciANN.

In deepXDE, I can use

rho0*tf.cast(tf.math.greater(((x-x_center_scaled)**2)/(x_axis_scaled**2),1),tf.float64)

To set a circle (line segment in 1D for now) in the center of the domain to zero while keeping everything else at a constant value. The result is shown below (sorry for the unlabeled axes - that is x from 0 to 75 and t from 0 to 10).

In SciANN, this doesn't seem to work since the Functionals cannot be acted on by TF operations. In accordance with the Burger eq example, I tried using

0.25*(1 - sign(tt - TOL)) * ((1 - sign(x - (left_boundary+TOL))) + (1 + sign(x - (right_boundary-TOL)))) * ( rho0)

as well as

0.5*(1 - sign(t - TOL)) * rho0 * sign(((x-x_center)**2)/(x_axis**2))

In numpy, both of these give the correct shape

I also tried using

0.5*(1 - sign(t - TOL)) * rho0 * tanh(((x-x_center)**2)/(x_axis**2))

Which should give a smoother boundary. In all cases the whole domain appears as solid rho0, with no area of 0 in the center, as shown below.

I also note that the initial condition loss seems to immediately get stuck at a particular value.

So I am wondering: is there a problem with the way I have set up my boundary conditions, a way to use TF operations or a "greater_than" function in SciANN, or is there another way to set up my boundary conditions?

Thanks, David