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BFGS results change with number of processors Date: 2010/12/02 19:13 Name: Sarah Jones   <sarah.jones@tyndall.ie> 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. Regards, 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 Hi, 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, TO

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