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> Hopefully your maximum step size and your tabulation step size are much
> larger than the step size sometimes used by the adaptive integrator.
> Here forcing results to come back at a fixed spacing forces you not to
> capture this signal properly in your graphs. This seems really
> unfortunate, you may have correctly integrated a complicated action
> potential and then you draw a graph which completely misses it! This
> seems really bad. Isn't it much better is to concentrate your line
> segments in your graph in exactly the same places where the adaptive
> step size system found your solution to be complicated?

yes. unless you need simulation results at exact values for whatever reason.

> If an integrator produces "different" results depending on the
> tabulation step size then it sounds as if it hasn't converged and so the
> adaptive step size isn't working, maybe your maximum step size needs to
> be further reduced for the problems you point out about missing the
> important part? If your tabulation is a multiple of your maximum step
> size as you suggested then I can't understand how this can happen.
> (I do realise that there are probably a number of models that are
> dependent on not being converged.)

Sorry, maybe I wasn't clear enough. Its not that your integration
results are different or not converged (assuming your maximum step size
is reasonable), the problem is the representation of the simulation
results that you are left with following the integration will be different.

I agree, ideally you want to have simulation data stored/drawn/whatever
say every 10 steps so you get high resolution where it is needed. But
depending on what you want to do with the simulation results you may
also want to be able to get simulation results evenly spaced in the
bound variable(s) domain.

> And if your integration solution is affected by the tabulated result
> spacing what if you don't want tabulated results? You just want the end
> integration, then you have to tell your integrator to generate some
> special tabulation just to get the same final state from your model?

I think I answered this above. The tabulation interval should definitely
not affect the actual results - only the maximum step size should do
that - it just changes the representation of the results. For this
example I'd imagine just setting the tabulation step size to take you to
the end point in one step.

> After thinking about where the interpolation should be performed, I
> expect that most integrators will end up interpolating somehow to
> generate values at the exact grid you specified, I do agree that the
> integrator may be able to give a far more accurate interpolation, as
> presumably it has a far finer set of values than the ones returned as
> results, however requiring a grid, specified in the model metadata,
> doesn't seem the best way to specify this.

Certainly most of the integrators I use internally maintain a history of
integration information to specifically allow such interpolation (within
reason).

I think the distinction here (which has only just started to occur to
me, sorry for being a bit slow this morning) is that for the
specification of the bound variable interval in a given simulation, the
start, end, and maximum step size values control the actual numerical
integration of the model. Whereas the tabulation information (however we
want to specify it) governs the representation of the simulation results
that you are left holding at the completion of the simulation.

In general, the tabulation specification is probably not all that
important for any given simulation. Where it does start to become
crucial is in the comparison of simulation results, either in the
comparison of different models or the comparison of results from the
same simulation using different tools.

So does this mean it shouldn't be in the simulation metadata
specification? I still don't see where else it could be. Although given
it is an optional property of a simulation and tools are not forced to
obey it when it is present I see no harm having it present. This then
allows tools to use that information if required to produce a very
specific representation of the simulation results.

> I didn't even bring this up yesterday as I was ignored last time I
> brought it up, but it really seems wrong to me to be forcing your
> integrator to give results on a grid in every case, and even more
> concerning to me if as you suggest, the performance of your model is
> dependent on this grid.

See comments above. I think we are only forcing the integrator to give
results on a grid if a specific representation of the simulation results
is required.

> However I am not a user or intended user of these ODE integrators. My
> experience only comes from the ODE integrator that I maintain in CMGUI
> which is for tracking streamlines and streaklines.
> So if I am outvoted I'll just take my concerns back into my hole.

you can't do that - you've convinced me now to stop blindly following
the tabulation step size unless I need to for some reason....who knows
what your next reply will accomplish?


Andre.

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• [cellml-discussion] Summary of simulation metadata meeting, Andrew Miller, 08/22/2006
  • [cellml-discussion] Summary of simulation metadata meeting, David Nickerson, 08/22/2006
    • [cellml-discussion] Summary of simulation metadata meeting, Shane Blackett, 08/23/2006
      • [cellml-discussion] Summary of simulation metadata meeting, David Nickerson, 08/23/2006
        • [cellml-discussion] Summary of simulation metadata meeting, Shane Blackett, 08/23/2006
          • [cellml-discussion] Summary of simulation metadata meeting, David Nickerson, 08/23/2006
          • [cellml-discussion] Summary of simulation metadata meeting, Andrew Miller, 08/30/2006

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