variance minimization in Casion

General discussion of the Cambridge quantum Monte Carlo code CASINO; how to install and setup; how to use it; what it does; applications.
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Katharina Doblhoff
Posts: 84
Joined: Tue Jun 17, 2014 6:50 am

variance minimization in Casion

Post by Katharina Doblhoff »

Sorry to come back to this old and boring topic, but I am still not sure what CASINO does internally when variance optimizing and how this compares to other codes.

Let me summarize what I THINK CASINO does. Please correct me, where I am wrong!
1.) For every optimization cycle, the correlation.out from the previous optimization is used as starting point
2.) For each optimization cycle nconfig_write configurations are created
3.) The local energy at each config is calculated and fed to nl2sno to compute a step in the parameters
4.) nl2sno suggests a step (change in parameters to be made)
5.) a.) If nl2sno believes that the relative change in variance will be below 1/sqrt(n_config_write), the optimization is stopped and we assume to have found the minimum.
b.) The new parameters are used to calculate the new local energies (at the same configs)
6.)a.) if the step leads to a reduction of the variance , the step is accepted and a nl2sno takes the next step (goto 3)
b.) if the step leads to an increase in variance, the step size is reduced. If the step size is not too small: goto 5b; else: stop optimization with message false convergence; assume mimimum is found and the message is due to numerical instabilities at the minimum.

Now let me compare that to what I THINK qwalk does:
Qwalk takes only one set of configurations (optimization cycle = 1) and optimizes a fixed number of times. The relative changes in variance observed can thereby be much smaller than 1/sqrt(nconfigs).

So the differences are: In CASINO the correlated sampling is not taken that far (optimization stops at a relative change of 1/sqrt(nconfigs) ), but on the other hand CASINO redoes the configs in a new cycle and adjusts the configs to the new wavefunction, thus hopefully better representing the the wavefunction even a finite number of walkers.

I would be very grateful if anybody could comment on the correctness/incorrectness of my understanding.
Thank you, Katharina
Vladimir_Konjkov
Posts: 165
Joined: Wed Apr 15, 2015 3:14 pm

Re: variance minimization in Casion

Post by Vladimir_Konjkov »

Hi, Katharina.

I have used QWALK and I can say that the JASTROW optimization in QWALK is much less stable than in CASINO. Especially if you start from default JASTROW parameters.
To tell the truth I was not able to optimize JASTROW parameters in QWALK for cubane if started form defaults.
So I prepare 1000 random sets of JASTROW parameters then found the best and than do JASTROW optimization from it. In that case all works fine and fast and gives me roughly the same energy as in CASINO.

I think my experience could be useful.

Vladimir.
In Soviet Russia Casino plays you.
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