# parameter optimization

Does anybody know of any tutorial material that explains how to use Mathematica to fit parameter values used in a set of ordinary differential equations to experimental values stored in a comma separated variable (CSV) file, and assumes very basic Mathematica programming experience?

The ordinary differential equations are required to provide a time course simulation of the variables that is fitted to experimental data, in order to use the parameter values to predict hypothesis on the behavior of the system.

Thanks for any assistance.

• @Steve Welcome to the forum. Please search the forum before you post a question!! Its happens often that the problem you are facing is already addressed before. Please look at this question mathematica.stackexchange.com/questions/6751/…. I hope this helps you. – PlatoManiac Jul 27 '12 at 17:27
• Also, it seems to me that you are posting two unrelated questions there. Please, if that is the case, separate them into two postings – Dr. belisarius Jul 27 '12 at 18:03
• Another issue: the etcs in your functions (they are not equations, are they?) are not clear enough for me – Dr. belisarius Jul 27 '12 at 18:04
• etc is "etcetera" to simplify what I was inserting. Sorry for posting a question that had been investigated in another post, if you are a moderator please feel free to delete this. I will investigate the forum post linked above and attempt to adapt it to my work. – Steve Jul 27 '12 at 18:44
• What does ODE stand for? – FredrikD Jul 27 '12 at 19:02

I am not sure if I am following your problem. Perhaps this is a partial answer.

For solving ODEs like yours for a variable number of functions, you could do something like:

dims = 3;
k = RandomInteger[{-2, 2}, {dims, dims}];
DSolve[Table[
D[f[i, x], x] == Table[f[j, x], {j, dims}].k[[i]] &&
(D[f[i, x], x] /. x -> 0) == 1, {i, dims}],
Table[f[j, x], {j, dims}], x]


which of course is solvable only in some cases

Plot[Table[f[i, x] /. sol[], {i, dims}], {x, 0, 1},Evaluated -> True] Note that the system you are solving is something like:

$\left\{f^{(0,1)}(1,x)=f(1,x) p[[1,1]]+f(2,x) p[[1,2]]+f(3,x) p[[1,3]]\land f^{(0,1)}(1,0)=1,\\ f^{(0,1)}(2,x)=f(1,x) p[[2,1]]+f(2,x) p[[2,2]]+f(3,x) p[[2,3]]\land f^{(0,1)}(2,0)=1, \\f^{(0,1)}(3,x)=f(1,x) p[[3,1]]+f(2,x) p[[3,2]]+f(3,x) p[[3,3]]\land f^{(0,1)}(3,0)=1\right\}$