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

[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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