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
er...@xray.bmc.uu.se http://xray.bmc.uu.se/molbiophys
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