[gmx-users] Estimation of the trajectory sampling from Covariance analysis

[Mark Abraham]

If your trajectory halves were fully converged then you would observe no
difference in their PCs. Since differences exist, your simulations cannot
possibly have converged. Convergence implies the same covariance matrix,
but unfortunately even if you had the same PCs, it's still a leap in the
dark to assume convergence. (For example, in a deep double-well potential,
each of two simulations could be trapped in a different well, and produce
the same covariance matrix, despite their temporal ensembles not being
identical, nor those ensembles resembling the thermodynamic ensemble.)

Mark

On Sat, Jan 19, 2013 at 8:44 PM, James Starlight <jmsstarlight at gmail.com>wrote:

> Dear Gromacs users!
>
>
> In the gromacs manual I found that "A good way to check the relevance
> of the first few principal modes is to calculate the overlap of the
> sampling between the first and second half of the simulation."
> Below you can see results of such overlap (inner product) between 2
> sub-spaces calculated from first and second part of my trajectory ( in
> the lowest frequency regime- only first 5 principal modes from both
> trajectories)
>
>
>                                                     MD Second Half of
> simulation
>                                                       #1     #2     #3
>     #4     #5
> MD first Half of simulation #1   +0.21  +0.68  +0.36  -0.33  -0.37
> MD first Half of simulation #2   -0.07  +0.13  +0.57  +0.30  +0.02
> MD first Half of simulation #3   +0.16  -0.22  +0.31  +0.20  -0.28
> MD first Half of simulation #4   +0.85  +0.22  -0.07  +0.02  -0.14
> MD first Half of simulation #5   +0.14  +0.40  -0.37  +0.49  -0.13
>
>
> Here you can see that 4rd PC from the first half of simulation
> correspond to the 1st PC from second half of simulation (+0.85). On
> the contrary 2nd mode from second half of simulation correspond to the
> 1st mode of first part of simulation (+0.68 ). Finally 3rd mode from
> second half of simulation corresponds to the second mode of the first
> mode. So it seems that during simulation there is some 'dynamics' in
> the lowest frequency regime (e.g I noticed that SEVERAL high frequency
> modes in the shorter trajectory during evolution of the system  join
> together forming ONE more slower mode in the longest trajectory). How
> this can be described from the physic points of view? And how exactly
> I can estimate the sampling quality of my complete trajectory ?
>
> Thanks for help,
> James
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