DMC timestep bias asymptotic

General discussion of quantum Monte Carlo in electronic structure theory
Neil Drummond
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Re: DMC timestep bias asymptotic

In these cases, instead of fitting a+b.tau^(1/2)+c.tau... to the DMC energy, it might be better to fit (a+b.tau+c.tau^2)/(1+D.tau) to the energy against time step tau. This describes a crossover between two different linear bias regimes.

Best wishes,

Neil.
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Re: DMC timestep bias asymptotic

Neil Drummond wrote:In these cases, instead of fitting a+b.tau^(1/2)+c.tau... to the DMC energy, it might be better to fit (a+b.tau+c.tau^2)/(1+D.tau) to the energy against time step tau. This describes a crossover between two different linear bias regimes.

Best wishes,

Neil.
woohoo excellent!
timestep bias
be2.png (7.78 KiB) Viewed 42065 times
but this is very bad news for me, because the correlation length is where the red line, and 1/(3*Z^2) is where the black.
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Neil Drummond
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Re: DMC timestep bias asymptotic

Thanks for sending the graph. I think I'll stick to plane waves and pseudopotentials...

Best wishes,

Neil.
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Re: DMC timestep bias asymptotic

Neil Drummond wrote:Thanks for sending the graph. I think I'll stick to plane waves and pseudopotentials...

Best wishes,

Neil.
Hello Neil

I want to make one very important comment for that fitting

E = (a+b.tau+c.tau^2)/(1+D.tau)

Where:
a is E at (tau->0)
b is slope at (tau->0)
c/d is slope at (tau->inf)

I interpolated all my data with this equation and got better or comparable to other eqs (within the error) results, but when the number of points at small tau is insufficient to determine the b value because error of b is compatible with its abs value, we can effectively set b=0 and then reinterpolate the data with simple equation. In this case we can nevertheless determine a with a small enough error and find out a parabolic-like dependence between E and tau at small tau.
This also explains many of the previously published E(tau) dependencies.

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Neil Drummond
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Re: DMC timestep bias asymptotic

Thanks very much for investigating this.

The slope at tau=0 is b-D.a, so setting b=0 doesn't get rid of the slope at tau=0 (but I can nevertheless believe that setting b=0 gives a reasonable fitting function for the situation you describe).

Best wishes,

Neil.
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Re: DMC timestep bias asymptotic

Cyrus_Umrigar wrote: Fri Mar 09, 2018 6:43 am If you look at Fig. 13 of Umrigar, Nightingale, Runge, J. Chem. Phys. 1993, you will see that it is nearly quadratic near tau=0.
I do not know of a theoretical argument for the behaviour of the time-step error.
What is the x-scale on your plots?

Cyrus
Hello Cyrus and everybody usnig QMC methods. In the process of implementing DMC in my program I would like to clarify way to calculate effective time step.
As described in the above link UNR (24) and also in Casino Manual 13.5.1 The effective time step (60):
Teff = averages are over all attempted moves of the electrons i in configuration α at time step m with weights of acceptance probability of the electron move. Then Teff used in UNR (23) to calculate branching factor of particular configuration.
What formula is required to calculate Teff in the case configuration-by-configuration sampling CBCS? In my guess Teff simply equals T in this case.

Also Teff using in timedependent normalization constant - Et, UNR (11) or Casino manual (58) whether it is necessary in this case to use Teff and by what formula to calculate it in case of CBCS?

In my calculations I do not use the weighted DMC so after branching each configuration has a weight = 1. In this way I replace averaging with weights by averaging after branching.

Another question about configuration that crossed the nodal surface and it`s move is rejected. Does acceptance probability UNR (22) for this configuration be set to 0 in UNR (24)?

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Neil Drummond
Posts: 97
Joined: Fri May 31, 2013 10:42 am
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Re: DMC timestep bias asymptotic

For configuration-by-configuration DMC (in CASINO at least), the effective time step for any particular configuration that has just moved is tau_eff=p.tau, where p is the configuration-move acceptance probability and tau is the real time step.

The mean effective time step tau_EFF=<tau_eff>, used when setting the reference energy E_T, is evaluated like any other expectation value.

CASINO does not use weighted DMC by default. It can be switched on by setting lwdmc to T.

Even in unweighted DMC, one still has to calculate move-acceptance probabilities.

The move acceptance probability for a node-crossing move is zero if complex_wf=F. In practice very few moves are rejected due to node-crossing attempts, and it doesn't really seem to matter what one does with node-crossing attempts. If complex_wf=T then we don't bother with this at all.

Hope this helps. Best wishes,

Neil.