Re: How to make fitting code using NDSolve?

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• Subject: [mg128433] Re: How to make fitting code using NDSolve?
• From: long.he.dragon at gmail.com
• Date: Fri, 19 Oct 2012 02:42:03 -0400 (EDT)
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• References: <k0sroq\$jn4\$1@smc.vnet.net>

```Hi   Yeom

I am facing some similar problem as yours.   Do you have any solution for your original post ?
Thanks for sharing

Long

On Monday, August 20, 2012 2:16:26 AM UTC-6, JYeom wrote:
> Hello,
>
> I am trying to fit some basic data to a partial differential equation- here are the data points:
>
>
>
> data = {
>
>   {2.113, 2.915*^-7}, {2.256, 2.758*^-7}, {2.303, 2.567*^-7}, {2.493,
>
>    2.343*^-7}, {2.635, 2.085*^-7}, {2.825, 1.838*^-7}, {3.015,
>
>    1.614*^-7}, {3.205, 1.412*^-7}, {3.538, 1.199*^-7}, {3.775,
>
>    1.03*^-7}, {4.108, 8.173*^-8}, {4.487, 6.266*^-8}, {4.915,
>
>    4.695*^-8}, {5.295, 3.349*^-8}, {5.912, 2.34*^-8}, {6.672,
>
>    1.554*^-8}, {7.527, 7.692*^-9}, {8.524, 5.448*^-9}, {9.426,
>
>    4.326*^-9}, {10.23, 3.205*^-9}, {10.99,
>
>    2.083*^-9}, {11.99, -1.608*^-10}
>
>   }
>
>
>
> And there are four parameters to fit in our fitting equation:
>
>
>
> model[ka_?NumberQ, kr_?NumberQ, kd_?NumberQ,
>
>   kb_?NumberQ] := (model[ka, kr, kd, kb] =
>
>    First[Subscript[Dye, 0] /. NDSolve[{
>
>        Derivative[1][Subscript[Dye, 0]][
>
>          t] ==\[VeryThinSpace]-ka Subscript[Dye, 0][t] +
>
>          kr  Subscript[Dyes, 0][t], Subscript[Dye, 0][0] == 1.22 10^-6,
>
>        Derivative[1][Subscript[Dye, 1]][
>
>          t] == -ka Subscript[Dye, 1][t] + kr  Subscript[Dyes, 1][t],
>
>        Subscript[Dye, 1][0] == 0,
>
>
>
>        Derivative[1][Subscript[Dyes, 0]][t] ==
>
>         ka  Subscript[Dye, 0][t] - kr  Subscript[Dyes, 0][t] -
>
>          kd  Subscript[CI, 0][t] Subscript[Dyes, 0][t] -
>
>          kd /2 * Subscript[CI, 1][t] Subscript[Dyes, 1][t],
>
>        Subscript[Dyes, 0][0] == 0,
>
>        Derivative[1][Subscript[Dyes, 1]][t] ==
>
>         ka Subscript[Dye, 1][t] -
>
>          kd Subscript[CI, 1][t] Subscript[Dyes, 0][t] -
>
>          kr Subscript[Dyes, 1][t] -
>
>          kd  Subscript[CI, 0][t] Subscript[Dyes, 1][t],
>
>        Subscript[Dyes, 1][0] == 0,
>
>
>
>        Derivative[1][Subscript[CI, 0]][
>
>          t] == -kd Subscript[CI, 0][t] Subscript[Dyes, 0][t] -
>
>          kd/2*  Subscript[CI, 1][t] Subscript[Dyes, 1][t] -
>
>          kb Subscript[CI, 0][t] Subscript[HDye, 0][t] -
>
>          kb/2* Subscript[CI, 1][t] Subscript[HDye, 1][t],
>
>        Subscript[CI, 0][0] == 3.18 10^-3,
>
>        Derivative[1][Subscript[CI, 1]][
>
>          t] == -kd Subscript[CI, 1][t] Subscript[Dyes, 0][t] -
>
>          kd/2*  Subscript[CI, 0][t] Subscript[Dyes, 1][t] -
>
>          kb Subscript[CI, 1][t] Subscript[HDye, 0][t] -
>
>          kb/2*Subscript[CI, 0][t] Subscript[HDye, 1][t],
>
>        Subscript[CI, 1][0] == 0,
>
>
>
>        Derivative[1][Subscript[HDye, 0]][t] ==
>
>         kd  Subscript[CI, 0][t] Subscript[Dyes, 0][t] +
>
>          kd/2* Subscript[CI, 1][t] Subscript[Dyes, 1][t] -
>
>          kb  Subscript[CI, 0][t] Subscript[HDye, 0][t] -
>
>          kb /2* Subscript[CI, 1][t] Subscript[HDye, 1][t],
>
>        Subscript[HDye, 0][0] == 0,
>
>        Derivative[1][Subscript[HDye, 1]][t] ==
>
>         kd  Subscript[CI, 1][t] Subscript[Dyes, 0][t] +
>
>          kd  Subscript[CI, 0][t] Subscript[Dyes, 1][t] -
>
>          kb Subscript[CI, 1][t] Subscript[HDye, 0][t] -
>
>          kb  Subscript[CI, 0][t] Subscript[HDye, 1][t],
>
>        Subscript[HDye, 1][0] == 0
>
>        }, {Subscript[Dye, 0][t], Subscript[Dyes, 0][t],
>
>        Subscript[CI, 0][t], Subscript[HDye, 0][t],
>
>        Subscript[Dye, 1][t], Subscript[Dyes, 1][t],
>
>        Subscript[CI, 1][t], Subscript[HDye, 1][t]}, {t, 0, 12}]])
>
>
>
> In the NDSolve, what we want to fit is Dye0[t]. So we wrote code for fitting using FindFit:
>
>
>
> fit = FindFit[data,
>
>   model[ ka, kr, kd, kb][Subscript[Dye,
>
>    0]], {{ka, 10^(-4)}, {kr, 10^(-4)}, {kd, 500}, {kb, 500}},
>
>   Subscript[Dye, 0]]
>
>
>
> However, we encountered the error message like this:
>
>
>
> FindFit::nrlnum: "The function value {-2.915*10^-7+Subscript[Dye, 0][2.113],-2.758*10^-7+Subscript[Dye, 0][2.256],-2.567*10^-7+Subscript[Dye, 0][2.303],<<16>>,-3.205*10^-9+Subscript[Dye, 0][10.23],-2.083*10^-9+Subscript[Dye,0][10.99],1.608*10^-10+Subscript[Dye, 0][11.99]} is not a list of real numbers with dimensions {22} at {ka,kr,kd,kb} = {0.0001,0.0001,500.,500.}."
>
>
>
> The desirable solution for parameter is around ka= 0.67, kr = 10^(-3), kd=1600, kb=1600.
>
>
>
> Does anyone know what I am doing wrong?

```

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