[gmx-developers] Drift in Conserved-Energy with Nose-Hoover thermostat

[Bernhard]

Please excuse me - for some reason the axis labels in the buffer-size 
vs- energy-drift plot got lost.
Here is the complete plot:
https://www.dropbox.com/s/otuijs1py55zmzh/buffersize-vs-total-energy-drift-1.png?dl=0

Am 21/07/15 um 14:40 schrieb Bernhard:
> Dear Michael,
>
> thank you very much for your very helpfull answer.
> Obviously we agree on the dubious nature of the linear drift and that 
> its origin from reduced precision round-off errors is doubtful.
> In my opinion the occurence of a linear energy drift of this size 
> could indicate a bug in the program.
> So I startet a more rigorous investigation and would like to share 
> some preliminary results:
>
> Graph of Verlet buffer-size vs. energy-drift size for single and 
> double precision:
> https://www.dropbox.com/s/e56916inlm0ym48/buffersize-vs-total-energy-drift.png?dl=0
>
> Graph of the linear total energy drift for a buffer-size of 0.02nm:
> https://www.dropbox.com/s/ifq3v3jwfzn4goh/4_nve_100ps_rlist-1.02_Total-Energy.png?dl=0
>
> Exemplary mdp and log files for a buffer-size of 0.02nm:
> https://www.dropbox.com/s/peamt27d2exhclc/4_nve_100ps_rlist-1.02.mdp?dl=0
> https://www.dropbox.com/s/70ictqb6nbs94wk/4_nve_100ps_rlist-1.02.log?dl=0
>
> The investigated protein-water system consists of 22765 atoms, the 
> AMBER99SB-ILDN force field with TIP3P water was used, all simulations 
> were in the NVE-ensemble, GROMACS 4.6.7 was used.
>
> I will repeat the tests with GROMACS 5.0 and for different test 
> systems (i.e. the lysozyme system from the popular lysozyme tutorial 
> of Justin Lemkul).
>
> Best,
> Bernhard
>
> Am 20/07/15 um 00:50 schrieb Shirts, Michael R. (mrs5pt):
>> > Do I have to switch to double precision if I care about energy 
>> conservation, integrator symplecticity, phase space volume 
>> conservation and ergodicity?
>>
>> This sounds a like a good idea.  If you are doing tests where this 
>> matters, use double precision. Sounds like the safest.
>>
>> > Since bigger round-off errors by reduced precision shouldn't 
>> accumulate linearly but at worst with Sqrt(N): Shouldn't one be 
>> worried about the occurence of a linear systematic error by only 
>> changing the precision from double to single in a calculation?
>>
>> Reduced precision errors only would be linear if the errors are 
>> uncorrelated, but it's not clear to me why roundoff errors would be 
>> uncorrelated.
>>
>> > But if you have a constant downward drift of energy you must 
>> consider that there is less phase space volume at lower energies - so 
>> there is no volume conservation in phase space.
>>
>> Correct, for NVE.  For NVT,  the conserved energy is a bookkeeping 
>> number, it has nothing to do with the current phase space of the 
>> system. The thermostat is pumping in more energy so that the kinetic 
>> energy remains consistent with the desired temperature.  We then 
>> actually have a steady state system, rather than an equilibrium 
>> system.  The question is, how different is this distribution from the 
>> true equilibrium distribution?
>>
>> This is generally testable.  For thermodynamic  calculations (which 
>> is what one presumably is intrested in with a thermostat, rather than 
>> the dynamics ), what really matters is 1) whether the correct 
>> distribution is obtained within noise and 2) whether the sampling is 
>> ergodic.  2) is very hard to answer, but 1) can be checked by
>>
>> https://github.com/shirtsgroup/checkensemble
>>
>> With the theory described here:
>>
>> http://dx.doi.org/10.1021/ct300688p
>>
>> Gromacs in single precisions seems to behave fine statistically for 
>> systems of a few hundred atoms.
>>
>> I suspect that there are subtle phenomena where the lack of exact 
>> symplecticness matters.  I also believe from my testing (no full 
>> paper on this) that there aren't very many that occur in highly 
>> chaotic systems with hundreds of particles at NIT.
>>
>> I bet there are cases with just a few particles where the problems 
>> could become very obvious, however.
>>
>> Best,
>> ~~~~~~~~~~~~
>> Michael Shirts
>> Associate Professor
>> Department of Chemical Engineering
>> University of Virginia
>> michael.shirts at virginia.edu <mailto:michael.shirts at virginia.edu>
>> (434) 243-1821
>>
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