Final bias reweighting + block analysis to assess convergenvce

[Eliane Briand]

Hi,

In some Plumed tutorials, we see the following protocol:  use the final bias to reweight frames in a metadynamic simulation, then using the weights for each frame to compute error as a function of block size. The plateauing of the error is a quantitative sign of convergence.

However, is it not a circular reasoning ? Final bias reweighting is correct only if the simulation is converged (according to the "Metadynamics with Adaptive Gaussians" paper), so if the simulation is not actually converged the first step is not legimitate and we cannot conclude that the simulation has converged from the block analysis. 

Is it a practical concern ? (Is it actually possible to have a seeemingly plateauing error curve even with a non-converged simulation, leading to false conclusions ?)

Best regard

[Giovanni Bussi]

Hi,

this is very similar to what happens with block analysis in general. If your simulation is not converged, you should notice that the estimated error *grows* with the block size instead of being stable. If you only make block analysis with, say, 5 blocks, you might not detect any problem.

There is a very simple example where this would be a problem: let's say you have two wells, you start filling well A and never visit well B. Clearly, you will not be able to estimate the free energy difference between A and B. A more subtle case would be that the system jumps to be at some point and never comes back. With properly done block analysis you should be able to detect the problem. But if you are not careful you might easily underestimate the error.

I would say that one has to *always* qualitatively check the simulation for transitions between the relevant states. Only after this has been done, it makes sense to compute the error with block analysis. In addition, with replica exchange one should check transitions in the "demuxed" trajectories.

I would also suggest to only use a part of the trajectory (in the past I often used the second half, or maybe the final 3/4) for this analysis. In this part usually the bias is not changing much (at least with well-tempered metadynamics), as it can be easily verified using sum_hills. If the bias is not changing much, the "final bias reweight" is equivalent to standard umbrella sampling reweighting and possibly to all other reweighting schemes available in the literature (this final statement is just a guess). An extreme way to apply this principle is to do "umbrella sampling refinement" on top of metadynamics, that is: stop adding hills at some point and only analyze the trajectory past that point. This is not too different to what happens with well-tempered metadynamics, where the bias grows less and less. What I find inconvenient of this approach is that it is more difficult to prolong a trajectory that is found to be not long enough.

I hope this answers your question!

Giovanni

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[Zeinasi]

Dear Giovanni, 

I have one naive (beginner) question regarding the block analysis method. 

In the Trieste tutorial, the first step in doing block analysis is using the plumed.dat (with PACE set to a bigger value) in combination with the plumed driver. At the end of this step, we should obtain a COLVAR file with the CVs and the value of the bias potential. 

In my case, when I was running the WT-METAD I printed the values of the CVs and metad.* (metad.bias and metad.rbias). In this case, I don't have to do the calculations again right (the step where we use a plumed file with a big PACE value) since I already have the values of metad.bias? 

Many thanks in advance for your clarifications.

Best, 

[Gareth Tribello]

Hello

I am not Giovanni but here goes.

You do need to run the calculation again if you want to use the final metadynamics bias in your reweighting.  The bias that you print out during the metadynamics is the instantaneous bias (i.e. V[s(t),t]).  We want the value of the FINAL bias though.  In other words: V(s(t), T) where T is the end of the simulation.  This value is different to V(s(t), t) as it is in the nature of metadynamics to add more bias as time moves on from t to the end of the simulation T.

Separately, use the information in this tutorial:

https://www.plumed.org/doc-v2.7/user-doc/html/masterclass-21-2.html

Rather than the Trieste tutorial.  There are some small differences between these instructions that are important.

Good luck

Gareth 

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[Zeinasi]

Thanks a lot, Gareth for the nice explanation! It's much clearer now! :)

Best,