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BFGS results change with number of processors
Date: 2010/12/02 19:13
Name: Sarah Jones   <>

Dear OpenMX developers,

I have noticed unusual behaviour of BFGS while performing scaling tests, the results changed with the number of processors used.

After the first optimisation step the results are almost the same:

cores Electronic Energy Total Energy Force
2 -179.3283044 -468.5445977 0.053797475
4 -179.3283041 -468.5445978 0.053797475
8 -179.3283048 -468.5445977 0.053797466
16 -179.3283061 -468.5445977 0.05379747
32 -179.3283060 -468.5445977 0.053797464

But after 100 optimisation steps there are considerable differences:

cores Electronic Energy Total Energy Force
2 -168.4415464 -469.0538697 0.000991008
4 -168.3503641 -469.0530458 0.0011273
8 -168.2833707 -468.9878693 0.053881706
16 -168.1067557 -468.3625791 0.309885448
32 -166.4478214 -468.19225 0.187456437

Following this, I continued to simulations to see if they converge to the same result. On 2 cores however, the structure started to break apart, while it converged in the other cases.

I repeated the same tests using EF and did not see this kind of behaviour.


Sarah Jones
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Re: BFGS results change with number of processors ( No.1 )
Date: 2010/12/02 23:23
Name: T.Ozaki


Thank you for your report.

I think that the behavior can be expected for the BFGS method.
Since the approximate Hessian by the BFGS method can possess even
negative eigenvalues, the ill-conditioned approximate Hessian allows
a structure to transit other structures through the quasi Newton update.
Also, it can be easily imagined that inverting the ill-conditioned approximate
Hessian, which may have nearly zero eigenvalues, tends to suffer from
numerical instability during long optimization steps, and also the type of
round-off error problem can be dependent on the number of processors for the
parallel calculations.

On the other hand, the EF method tries to eliminate the ill-conditioned
eigenstates of the approximate Hessian, leading to numerical stability.
Your observation may be the case.

Best regards,


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