PDE with small coefficient

[bahrami4444]

Thanks to Dr. Lu @lululxvi for providing this simple and powerful software.

I want to model the following equations in DeepXDE.

These equations are coupled and are coded as follows:

def PDE(Input, Output):
    
    u_yy = dde.grad.hessian(Output, Input, i=0, j=0, component=0)
    u_ty = dde.grad.hessian(Output, Input, i=0, j=1, component=0)
    p_yy = dde.grad.hessian(Output, Input, i=0, j=0, component=1)
    p_y = dde.grad.jacobian(Output, Input, i=1, j=0)
    p_t = dde.grad.jacobian(Output, Input, i=1, j=1)
    
    return [(λ + 2 * μ) * u_yy - α * p_y, α * u_ty + φ * β * p_t - κ * p_yy]

My problem is that the beta coefficient is too small (4.4e-4), and therefore the neural network cannot train properly. When I set beta to 1, the output of the neural network becomes logical (but incorrect). The figure below shows the logical answer:

And this figure represents the case when the real value of beta is applied:

Does anyone know how to fix this problem?

Using a dimensionless governing equation is not a good solution because, in such equations, t and z (space and time) become dimensionless, but the value of the beta coefficient remains small.
Scaling all coefficients also makes the other coefficients either too small or too large.
I also significantly reduced the learning rate and increased the number of layers, but the problem was not solved.

Please guide me.
Thanks.