Re: Identifying time-points at which the modelbecomes stiff

Hi Andrew,

Are you thinking that you'd have metadata like "when variable IStim is 
non-zero reduce maxDt to x" or more like "when variable IStim is 
non-zero system becomes stiff" and let the software decide the best way 
to handle that? I guess these are not exclusive choices, but the first 
one probably belongs in the simulation metadata whereas the second could 
be external to the simulation metadata.

Might also be worth noting that there will probably be overlap with the 
TEDDY project when representing this kind of information, but not really 
too sure yet where TEDDY is going.


Andre.


Andrew Miller wrote:
> Hi all,
> 
> A common issue a lot of CellML models face is that they have points at 
> which they go from being non-stiff (from the point of view of a 
> numerical algorithm), and then a sudden change happens. This change is 
> often due to a piecewise function (i.e. the model is actually 
> non-differentiable at the point).
> 
> As it is desirable to have stimulus currents and the like on for the 
> shortest time possible, so you can see what the model itself does 
> immediately after the stimulus, the only way around this at the moment 
> is to set the maximum step size of your integrator algorithm very low 
> (or, for example, tweak error control parameters to stop the step size 
> from getting so low).
> 
> The problem with this is that the stimulus actually only occurs for a 
> very small proportion of the total run time of the model, so this is 
> needlessly slow. If there was a way to identify the bound variable 
> values at which we definitely want to evaluate, we could then ensure 
> that the integrator stops on that exact value. This would allow us to 
> even have singularities (for example, supporting singularity reset rules 
> following the reset rule MathML pattern I recently proposed).
> 
> There are two potential approaches:
> 1) Attempt to automatically determine the values at which the applicable 
> piece in piecewise equations changes (analytic determination). This can 
> be done for certain restricted cases, but in general is not feasible 
> (and would probably require finding an analytic solution of the system 
> in some cases, such as when variables other than the bound variable are 
> involved). To get around this, we would have to define a standard set 
> for which model authors can expect this behaviour to work.
> 2) Provide a metadata specification which provides additional 
> information to help simulators find singularities or other special time 
> points.
> 
> Because of the problems with the general case in 1, I prefer the second 
> option. However, there are still difficulties:
> i) How do you specify the points? Listing explicit points is not very 
> good, because it doesn't generalise well to PDEs, and there might be 
> infinitely many such points. The time points might also depend on 
> parameters, and you would want these to automatically update when you 
> re-parameterise the model. You would probably need to allow mathematical 
> expressions of some form to be referenced from the metadata, but we 
> would still want to provide a clean separation between data and metadata.
> ii) What about the case where the modeller doesn't know analytically at 
> what bound variable value something happens, but only a condition 
> involving some other variables (for example, the yeast cell cycle model 
> has state variables which, when they reach a threshold, cause the cell 
> to divide)? In this case, it would still be useful to provide some sort 
> of advance warning to the simulator of the condition. For example, the 
> modeller could provide a function which becomes zero at special points, 
> but further away, is non-zero, and doesn't show the same sort of 
> discontinuity that the rates show.
> 
> Are there any suggestions or opinions on how this case should best be 
> handled?
> 
> Best regards,
> Andrew
> 
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-- 
David Nickerson, PhD
Research Fellow
Division of Bioengineering
Faculty of Engineering
National University of Singapore
Email: david.nickerson-6Bl98Hp8bEiLvajZxc+D7Q@xxxxxxxxxxxxxxxx