[Libmesh-users] about the error bound estimated by SCM

[강다영 <dyd...@pu...>]

Dear all,

Hi,
I have a question about the error bound estimated by SCM in libmesh.

My model has three parameters, four subdomains with no geometric
parameterization, and a DOF near 20,000.
I did SCM training with this model and checked that the output error bound
somehow gave a negative value at some parameters.
However, I believe it is not plausible to have a "negative" value for the
error bound because the bound may stem from the norm value.

At first, I used 1000 SCM samples, and SCM gave a negative error bound even
at the reference parameter.
Then I tried more samples, i.e., 3000. In this case, the error bound at the
reference parameter was all positive. But still, it was negative at some
parameters like maximum and minimum parameters.

Apparently, it seems like more samples decrease the cases that give minus
error bound. But the problem is that the SCM training takes too much time.
For 3000 samples, it took nearly five days only for SCM training. Now I'm
trying with 6000 samples, and I guess it will take much more time.

I hope more samples will solve the negative bound problem anyway, but I
still wonder how it is possible to have a minus value for the error bound.
Could you give me some information to avoid this problem?

Furthermore, is there any rule of thumb for the number of SCM samples?
For now, I'm just randomly increasing the number of samples.

I'd be very much grateful if someone could give me any comments on this.

Best regards,
Dayoung Kang