Pedro Mendes wrote:
> On 31 Aug 97 at 16:54, Petr Kuzmic wrote:
> (...) How does the numerical approach fit into MCA?
> (...)
> It fits in several MODERN programs such as my own, Gepasi.
Very impressive package, congratulations!
> > Haven't we
> > (effectively) "moved from the ideal case ... to real ones" ever since Alan
> > Hindmarsh [Hind8355,Byrn8701] designed his collection of ODE solvers?
>> Indeed these solvers are extremely sophisticated and can cope with quite a
> high degree of stiffness. (...) I haven't found one
> example so stiff that it would not be able to solve it.
Unfortunately I did. I'll mail you the example when I dig it out of my
backups. The trouble is encountered during regression of experimental
data. Depending on the least-squares minimization algorithm, you may
transiently visit areas of the parameter space where association rate
constants acquire huge values, quite unrealistic to be sure but still
the machine wants to examine the sum of squares there.
I circumvented the problem in my least-squares fitter DYNAFIT
(http://www.biokin.com/dynafit/index.shtml), which uses the LSODE
solver, by some extra bookkeeping: if a step in the least-squares
minimization fails because the model could not be evaluated (probably
due to stiffness), I just pretend that the sum of squares increased in
that step and order the minimizer to take appropriate measures.
Another solution is 'constrained optimization' where each parameter is
given a 'trust region' (say all rate constants can change at most by a
factor of 10 in each step).
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Petr Kuzmic, Ph.D. | (608) 256-4790
BioKin Consulting | fax (708) 256-1269
P.O. Box 8336 | pkuzmic at biokin.com
Madison WI 53708 | http://www.biokin.com
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