PointSetBC() doubt

[guimilhoratti]

Hi all,

I am using boundary_conditions.PointSetBC() in my code, however, I am unsure if I understand how it works.

It seems that it generates Dirichlet boundary conditions from the exact solution.

1-Does it use border data from the solution?
2-Does it calculate boundary loss using each point and its respective solution result?
3-How can I learn more about it?

Best Regards,

[ryabs07]

Hi,
I think this example of inverse problem is a pretty good for understanding execution of PointSetBC.

A snippet of code from the example:

observe_x = np.vstack((np.linspace(-1, 1, num=10), np.full((10), 1))).T
observe_y = dde.icbc.PointSetBC(observe_x, func(observe_x), component=0)

data = dde.data.TimePDE(
    geomtime,
    pde,
    [bc, ic, observe_y],
    num_domain=40,
    num_boundary=20,
    num_initial=10,
    anchors=observe_x,
    solution=func,
    num_test=10000,
)

observe_x is an array of input points for which you have observed values observe_y (you can input just the boundary points if you strictly want to use it for BC).

[ryabs07]

yes exactly. how are the results coming along for you using PointSetBC? For me, the loss for this supervised training portion stops decreasing after couple of hundred iterations and the results are quite bad.

[guimilhoratti]

My results are bad and the supervisory training has plateaued after a thousand iterations. Have you tried using a smaller dataset?

[ryabs07]

I was trying to use PointSetBC for initial condition only and I had barely 300 points. I face the same issue. I have tried multiple hyperparameters, but nothing seems to work. I have posted the problem in the discussions, hopefully someone experienced can give us some suggestions.

[guimilhoratti]

I hope so, local minima make things complicated

[ryabs07]

Hi again,
Have you had any success with the issue of plateau when youre training with PointSetBC?

[guimilhoratti]

Hi,
I believe my results are enough accurately to my problem (I hope so).
I did not test other changes.

What about you?

[ryabs07]

PointSetBC is working for inverse problems for me. However, the training still plateaus for forward problems with semi-supervised training.

[guimilhoratti]

I see,

My case is an inverse problem, and PointsetBC() is working so far. I have not tryed a forward problem.

How many scattered points and data points are you using?

It would be good if we exchanged experiences. :)

Thank you