How does one use a fitting routine such as NonlinearModelFit with a ParametricFunction? Example below:

First let's generate some data:

sample[t_] = (0.002 + 101 t - 461000 t^2 + 2.218 10^9 t^3 - 3.64 10^12 t^4 + 3.17 10^15 t^5 ) Exp[-8653 t]; data = Table[{t, sample[t] + RandomVariate[NormalDistribution[0, 0.00001]]}, {t, 0, 0.002, 0.000004}]; ListPlot[data] 

Now lets define a model:

rateeqs = {a'[t] == -k1a a[t] - k12 a[t] c70gs + k21 b[t] c60gs, b'[t] == -k1b b[t] - k21 b[t] c60gs + k12 a[t] c70gs, a[0] == a0, b[0] == b0}; c60gs = c70gs = 5; maxTime = 0.0025; e60 = 19060; e70 = 948; fitFunc[t_] = \[Epsilon]60 a[t] + \[Epsilon]70 b[t]; params = {k1a, k1b, k12, k21, a0, b0}; initGuesses = {8000, 100, 4500, 2000, 5. 10^-8, 8 10^-7}; 

Now we generate a parametric solution to the model:

solution[t_] = ParametricNDSolveValue[rateeqs, fitFunc[t], {t, 0, maxTime}, params, WorkingPrecision->30] 

And we verify that the solution works:

Show[ListPlot[data, PlotStyle -> Red, PlotRange -> Full], Plot[(solution[t] @@ initGuesses), {t, 0, maxTime}]] 

It would seem that I should be able to fit this model to the sample data starting from the initGuesses values for the parameters using something like this:

modelFit = NonlinearModelFit[data, solution[t] @@ params, {params, initGuesses}\[Transpose], t]; 

But I get errors:

I'm sure it's a syntax issue, but I have tried so many different possibilities that the screen is swimming in front of my eyes. Any help is appreciated!

How does one use a fitting routine such as NonlinearModelFit with a ParametricFunction? Example below:

First let's generate some data:

sample[t_] = (0.002 + 101 t - 461000 t^2 + 2.218 10^9 t^3 - 3.64 10^12 t^4 + 3.17 10^15 t^5 ) Exp[-8653 t]; data = Table[{t, sample[t] + RandomVariate[NormalDistribution[0, 0.00001]]}, {t, 0, 0.002, 0.000004}]; ListPlot[data] 

Now lets define a model:

rateeqs = {a'[t] == -k1a a[t] - k12 a[t] c70gs + k21 b[t] c60gs, b'[t] == -k1b b[t] - k21 b[t] c60gs + k12 a[t] c70gs, a[0] == a0, b[0] == b0}; c60gs = c70gs = 5; maxTime = 0.0025; e60 = 19060; e70 = 948; fitFunc[t_] = e60 a[t] + e70 b[t]; params = {k1a, k1b, k12, k21, a0, b0}; initGuesses = {8000, 100, 4500, 2000, 5. 10^-8, 8 10^-7}; 

Now we generate a parametric solution to the model:

solution[t_] = ParametricNDSolveValue[rateeqs, fitFunc[t], {t, 0, maxTime}, params, WorkingPrecision->30] 

And we verify that the solution works:

Show[ListPlot[data, PlotStyle -> Red, PlotRange -> Full], Plot[(solution[t] @@ initGuesses), {t, 0, maxTime}]] 

It would seem that I should be able to fit this model to the sample data starting from the initGuesses values for the parameters using something like this:

modelFit = NonlinearModelFit[data, solution[t] @@ params, {params, initGuesses}\[Transpose], t]; 

But I get errors:

I'm sure it's a syntax issue, but I have tried so many different possibilities that the screen is swimming in front of my eyes. Any help is appreciated!