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 _______________________________________________ cellml-discussion mailing list [email protected] http://www.cellml.org/mailman/listinfo/cellml-discussion
