[gmx-users] Same starting structure but different trajectories

[Erik Marklund]

The times when registers are pushed to the stack may happen at different 
points in the calculations in different runs, so the "bonus accuracy" 
may be lost at different times. As I mentioned, a hardware interrupt may 
(will) force such an event, and this may be due to some external 
trigger, such as a mouse click or a keystroke.

Note that there are other sources of discrepancy than the one I 
mentioned (and I'm not sure if that's even a common thing to find in 
modern AMD or Intel cpus, it's just an example). If you run your 
simulation in parallel, then the order that the processeses finish 
certain tasks may affect the outcome of certain floating point 
additions. In general, for floats (A+B)+C != A+(B+C), so if you have 
three processes that coimpute e.g. the kinetic energy for parts of your 
system, and the values are summed up by the MPI library, then the order 
of the summation may depend on the order in which the processes finish.

As for the numerical chaos. It is all about the long term sensitivity to 
small differences in the initial conditions. Errors at time t can be 
estimated by factor exp(lambda*t), where lambda is the Lyapunov 
exponent. If lambda is larger than one then your error will increase 
exponentially, however small the initial error,a nd the system is thus 
chaotic. For n-body problems, like the ones we have in MD, even the 
analytic solutions are often chaotic.

In general, the hardware side of things is increadibly more complicated 
than what you may first think as a programmer.

Hope that helps your understanding.

/Erik

Emanuel Peter skrev:
> Dear Erik,
>
> I still have some trouble to understand. 
> Could you give me a more detailed answer why I get two different 
> trajectories on the same machine? It should have the same registers and 
> numerical chaos should be exactly the same in that case.
>
> Bests,
>
> Emanuel
>
>   
>>>> Erik Marklund  02/17/10 10:05 AM >>>
>>>>         
> Well, unfortunately it doesn't. Numerical differences are introduced 
> here and there for different resasons. On some machines the registers 
> have more bits than you'd normally fit into a float or double, and hence 
> give higher precision. If those registers are pushed to the stack, then 
> the trailing bits get lost. This can happen due to thread scheduling or 
> hardware interrupts. Such small differences between runs will over time 
> build up to arbitrarily large differences because of the (numerically) 
> chaotic nature of MD simulations. When a program is parallelized even 
> more sources of such differences arise, since it's e.g. not known 
> beforehand in which order certain floats/doubles are added together, 
> which in turn may have a small effect on the results.
>
> /Erik
>
> Emanuel Peter skrev:
>   
>> Hi Tsjerk,
>>
>> I ran my job on the same machine and made exactly the same inputstructure and 
>> inputfile. 
>> What does chaos mean in your opinion? A computer should do exactly the same 
>> every time you start with the same starting conditions on the same machine.  
>>
>> I have to couple my ligand seperately and not as part of my protein, so I can't 
>> couple just two groups named Protein and Non-Protein.  
>>
>> Bests,
>>
>> Emanuel 
>>  
>>   
>>     
>>>>> Tsjerk Wassenaar  02/17/10 9:40 AM >>>
>>>>>         
>>>>>           
>> Hi Emanuel,
>>
>> Anything small can cause trajectories to diverge, it's chaos. The
>> machine on which is run can make the difference. This is also covered
>> in the list archives.
>>
>>   
>>     
>>> ;Temperature coupling
>>> tcoupl           = nose-hoover
>>> tc-grps          = protein NA+ CFP SOL
>>> tau_t             = 0.1  0.1 0.1   0.1
>>> ref_t             = 300 300 300 300
>>>     
>>>       
>> This is bad practice. Where did you get that from? Not from any _good_
>> tutorial, surely. Check
>> http://www.gromacs.org/Documentation/Terminology/Thermostats to learn
>> more.
>>
>> Cheers,
>>
>> Tsjerk
>>
>>
>>   
>>     
>
>
>   


-- 
-----------------------------------------------
Erik Marklund, PhD student
Laboratory of Molecular Biophysics,
Dept. of Cell and Molecular Biology, Uppsala University.
Husargatan 3, Box 596,    75124 Uppsala, Sweden
phone:    +46 18 471 4537        fax: +46 18 511 755
erikm at xray.bmc.uu.se    http://xray.bmc.uu.se/molbiophys