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

[David K. <dav...@ak...>]

Hi,

Thanks for your comments. I don't know the answers here. The SCM is needed
in order to get rigorous error bounds, but as you see here it is
complicated and can be computationally intensive, so a lot of people just
skip it. In order to get to the bottom of your issues, you'd have to
investigate more deeply what is happening to cause these issues (e.g. print
out a lot of information from what is happening as you run the SCM), and
see if you can diagnose the issue and improve it.

So I'm afraid I don't have much other advice here, other than these kinds
of difficulties are quite common with SCM in my experience, which is why
people often skip it.

Regards,
David


On Thu, Apr 28, 2022 at 9:51 AM 강다영 <dyd...@pu...> wrote:

> 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
>
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