Autotest for cutoffs optimization

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Autotest for cutoffs optimization

Postby Vladimir_Konjkov » Fri May 01, 2020 3:07 pm

Hello casino developers

I encountered a not completely clear issue in the latest version - JASTROW cutoff values are either not optimized at all or optimized worse than in previous CASINO versions.

I tried to understand whether this case is checked in autotests and how, but I did not find it.
Perhaps this is difficult to verify due to the random value of optimized VMC energy, but now even for simple monatomic systems the optimized VMC energies are underestimated by a dozen standard errors.

I will be grateful if you help me write the appropriate autotest.

Best Vladimir.

PS: I apologize that my post is again in the top.
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Re: Autotest for cutoffs optimization

Postby Pablo_Lopez_Rios » Fri May 01, 2020 3:28 pm

Hi Vladimir,

Could you post input/output files for an example in which the Jastrow cutoffs are well optimised by an older version (which?) and poorly optimised by the latest version of CASINO?

Thanks,
Pablo
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Re: Autotest for cutoffs optimization

Postby Neil Drummond » Fri May 01, 2020 8:08 pm

Dear Vladimir,

Here's a very quick test. For a 27-electron r_s=4 3D electron gas with a Jastrow factor containing a U term only, if I start from a cutoff length of L=4 a.u. and optimise the linear parameters together with the cutoff using variance minimisation:

Code: Select all
  VMC #1: E     = -0.0497(1) ; var  = 1.30(4) (correlation.out.0)
  VMC #2: E     = -0.06432(9) ; var  = 0.395(6) (correlation.out.1)
  VMC #3: E     = -0.06907(7) ; var  = 0.247(3) (correlation.out.2)
  VMC #4: E     = -0.07327(5) ; var  = 0.134(2) (correlation.out.3)
  VMC #5: E     = -0.07340(5) ; var  = 0.124(2) (correlation.out.4)
  VMC #6: E     = -0.07581(3) ; var  = 0.0552(8) (correlation.out.5)
  VMC #7: E     = -0.07644(3) ; var  = 0.0401(8) (correlation.out.6)
  VMC #8: E     = -0.07637(3) ; var  = 0.0397(8) (correlation.out.7)
  VMC #9: E     = -0.07639(3) ; var  = 0.0397(8) (correlation.out.8)


C.f., if L is fixed:

Code: Select all
  VMC #1: E     = -0.0500(2) ; var  = 1.34(7) (correlation.out.0)
  VMC #2: E     = -0.0578(1) ; var  = 0.612(7) (correlation.out.1)
  VMC #3: E     = -0.0580(1) ; var  = 0.613(7) (correlation.out.2)
  VMC #4: E     = -0.0581(1) ; var  = 0.614(7) (correlation.out.3)
  VMC #5: E     = -0.0582(1) ; var  = 0.603(7) (correlation.out.4)
  VMC #6: E     = -0.0578(1) ; var  = 0.609(7) (correlation.out.5)
  VMC #7: E     = -0.0578(1) ; var  = 0.610(7) (correlation.out.6)
  VMC #8: E     = -0.0578(1) ; var  = 0.615(7) (correlation.out.7)
  VMC #9: E     = -0.0577(1) ; var  = 0.627(9) (correlation.out.8)


So optimising the cutoff length does seem to work in this case at least.

Best wishes,

Neil.
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Re: Autotest for cutoffs optimization

Postby Vladimir_Konjkov » Sat May 02, 2020 1:48 am

Pablo_Lopez_Rios wrote:Hi Vladimir,

Could you post input/output files for an example in which the Jastrow cutoffs are well optimised by an older version (which?) and poorly optimised by the latest version of CASINO?

Thanks,
Pablo


Yes, here is a simple example that I found - old version and new version
8_8_44__test.tgz
new version
(63.37 KiB) Downloaded 72 times
archive symlinks point to the same files in the old version.

old VMC energy
Code: Select all
 VMC #1: E     = -24.531(5) ; var  = 5.2(4) (correlation.out.0, parameters.0.casl)
 VMC #2: E     = -24.6101(7) ; var  = 0.111(1) (correlation.out.1, parameters.1.casl)
 VMC #3: E     = -24.6208(7) ; var  = 0.1724(9) (correlation.out.2, parameters.2.casl)
 VMC #4: E     = -24.6214(7) ; var  = 0.179(2) (correlation.out.3, parameters.3.casl)
 VMC #5: E     = -24.6240(7) ; var  = 0.179(1) (correlation.out.4, parameters.4.casl)
 VMC #6: E     = -24.6240(9) ; var  = 0.3(2) (correlation.out.5, parameters.5.casl)
 VMC #7: E     = -24.6244(7) ; var  = 0.168(1) (correlation.out.6, parameters.6.casl)
 VMC #8: E     = -24.6242(7) ; var  = 0.169(2) (correlation.out.7, parameters.7.casl)
 VMC #9: E     = -24.6240(7) ; var  = 0.171(3) (correlation.out.8, parameters.8.casl)
 VMC #10: E     = -24.6244(7) ; var  = 0.170(1) (correlation.out.9, parameters.9.casl)


new VMC energy
Code: Select all
 VMC #1: E     = -24.527(5) ; var  = 5.2(3) (correlation.out.0, parameters.0.casl)
 VMC #2: E     = -24.6110(8) ; var  = 0.163(1) (correlation.out.1, parameters.1.casl)
 VMC #3: E     = -24.6117(8) ; var  = 0.167(1) (correlation.out.2, parameters.2.casl)
 VMC #4: E     = -24.6118(8) ; var  = 0.183(1) (correlation.out.3, parameters.3.casl)
 VMC #5: E     = -24.6155(8) ; var  = 0.190(1) (correlation.out.4, parameters.4.casl)
 VMC #6: E     = -24.6149(8) ; var  = 0.191(2) (correlation.out.5, parameters.5.casl)
 VMC #7: E     = -24.6154(8) ; var  = 0.190(1) (correlation.out.6, parameters.6.casl)
 VMC #8: E     = -24.6147(8) ; var  = 0.192(2) (correlation.out.7, parameters.7.casl)
 VMC #9: E     = -24.6149(8) ; var  = 0.191(2) (correlation.out.8, parameters.8.casl)
 VMC #10: E     = -24.6154(8) ; var  = 0.192(3) (correlation.out.9, parameters.9.casl)


I haven’t done calculations for a long time so I can’t say exactly when an issue occurred.

Best Vladimir.
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Re: Autotest for cutoffs optimization

Postby Pablo_Lopez_Rios » Sat May 02, 2020 7:03 pm

Hi Vladimir,

After a quick bisect, this seems to be due to commit v2.13.819 (a1a58085 by Neil) in which some BLAS calls were replaced with inline code. Maybe this commit just introduced numerical instabilities hindering the optimisation of gjastrow cut-offs, but it might be worth verifying that this is not a bug, and perhaps check if undoing the changes to the gjastrow and gbasis modules fixes this.

Best,
Pablo
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Re: Autotest for cutoffs optimization

Postby Neil Drummond » Sat May 02, 2020 10:22 pm

Dear Both,

Optimisation of cutoff lengths has always been challenging and numerically sensitive. These days I tend to fix the cutoff lengths at sensible values rather than attempt to optimise them. In the present case, fixing L_u=10, L_chi=8 and L_f=7 a.u. works OK:

Code: Select all
  VMC #1: E     = -24.588(2) ; var  = 0.809(4) (correlation.out.0)
  VMC #2: E     = -24.625(1) ; var  = 0.177(2) (correlation.out.1)
  VMC #3: E     = -24.624(1) ; var  = 0.176(1) (correlation.out.2)
  VMC #4: E     = -24.625(1) ; var  = 0.180(3) (correlation.out.3)
  VMC #5: E     = -24.625(1) ; var  = 0.177(2) (correlation.out.4)
  VMC #6: E     = -24.626(1) ; var  = 0.176(1) (correlation.out.5)
  VMC #7: E     = -24.628(1) ; var  = 0.180(2) (correlation.out.6)
  VMC #8: E     = -24.627(1) ; var  = 0.178(3) (correlation.out.7)
  VMC #9: E     = -24.6264(8) ; var  = 0.177(1) (correlation.out.8)


Using different f terms for parallel and antiparallel spin pairs gives slightly better results:

Code: Select all
  VMC #1: E     = -24.601(1) ; var  = 0.278(1) (correlation.out.0)
  VMC #2: E     = -24.6276(9) ; var  = 0.17(5) (correlation.out.1)
  VMC #3: E     = -24.6297(8) ; var  = 0.135(1) (correlation.out.2)
  VMC #4: E     = -24.6303(8) ; var  = 0.138(2) (correlation.out.3)
  VMC #5: E     = -24.6292(8) ; var  = 0.137(2) (correlation.out.4)


Best wishes,

Neil.
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Re: Autotest for cutoffs optimization

Postby Vladimir_Konjkov » Sun May 03, 2020 4:54 am

thanks Nail for intriguing me...I used the CASL format so there are no u, chi, f terms, at least in the configuration file.

For each maximum degree of polynomial approximation of each term there is an optimal cutoff.

Is it possible to see the complete set of files for the above example, and it is also interesting how the WFN was obtained.

I tried to figure out how much better JASTROW approximation improves the quality of subsequent BACKFLOW approximation.

Best Vladimir.
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Re: Autotest for cutoffs optimization

Postby Neil Drummond » Sun May 03, 2020 8:22 am

Dear Vladimir,

The form of Jastrow that you are using is essentially the same that I used: the three terms in your Jastrow factor are u (homogeneous electron-electron), chi (electron-nucleus) and f (electron-electron-nucleus).

Best wishes,

Neil.
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Re: Autotest for cutoffs optimization

Postby Vladimir_Konjkov » Mon May 04, 2020 5:21 am

Neil Drummond wrote:Dear Vladimir,

The form of Jastrow that you are using is essentially the same that I used: the three terms in your Jastrow factor are u (homogeneous electron-electron), chi (electron-nucleus) and f (electron-electron-nucleus).

Best wishes,

Neil.


I meant that JASTROW factor in CASINO can be described in two significantly different formats - "Drummond-Towler-Needs form" or "Pablo Lopez Rios form"

I made additional calculations and found out that for the first form, optimization of cutoffs works, but for the second one it doesn’t, as Pablo wrote after commit v2.13.819.

Best Vladimir.
In Soviet Russia Casino plays you.
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Posts: 134
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Re: Autotest for cutoffs optimization

Postby Neil Drummond » Mon May 04, 2020 3:02 pm

Dear Vladimir & Pablo,

You're right: I broke gjastrow optimisation in the patch that Pablo indicated. I've just sent a patch fixing the issue to Mike. Thanks very much for pointing out the problem, and I'm very sorry about the inconvenience.

The above results of playing around with the pjastrow wave function still apply, however: you can get a good wave function by fixing the cutoff lengths at a plausible value, and there is scope for improving the wave function by using different electron-electron-nucleus terms for parallel and antiparallel spins. Bases other than natural powers (available in gjastrow) might give further improvements to the wave function for an isolated atom.

Best wishes,

Neil.
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