Simultaneously Fit Multiple Data Sets

Questions
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1

Hi,

Is it possible to use FindFit or similar functions to simultaneously fit multiple data sets. For example in the code below I have a model
that I want to fit to two sets of experimental data. Using Map I can individually use FindFit to fit each data set. However I am wondering
if it’s possible to find one total set of best fit parameters for both data sets using these functions?
Procedurally, I would write a function that chooses a set of parameters and then measures the distance between the model and both data sets for that particular
parameter set. Is this possible with the built in functions?

Cheers!

texp = {0.2, 2.2, 4.0, 5.0, 6.0, 8.0, 11.0, 15.0, 18.0, 26.0, 33.0, 
   39.0, 45.0};
dexp = {35., 25., 22.1, 17.9, 16.8, 13.7, 12.4, 7.5, 4.9, 4.0, 2.4, 
   1.4, 1.1};
dt = Transpose[{texp, dexp}];
dt2 = Transpose[{texp, dexp - 0.75}];
model = ParametricNDSolveValue[{
   A'[t] == -ka*A[t],
   B'[t] == ka*A[t] - kb*B[t],
   c'[t] == kb*B[t],
   A[0] == 35.,
   B[0] == 0.,
   c[0] == 0.},
   A,
  {t, 0., 50.},
  {ka, kb}]
Map[FindFit[#, model[ka, kb][t], {{ka, 0.1}, {kb, 0.2}}, t] &, {dt, dt2}]
2

Hi Pat,

I had a similar problem some time ago. The best way to do what you want to do I think is the following. Do data=Join[dt,dt2] but here dt2 is not your dt2 original data, do a shift (for instance add 100) on the texp data which enters into the dt2 data. Then define a new model through the command NewModel:=If[texp<100,model,model[t-100]]. Thus FindFit[data,NewModel,{ka,kb},t]. Initial conditions for the parameters is up to you (recommendable).

Regards

3

Popular question. See fitting different data sets with different models with NonlinearModelFit
and links therein for more suggestions.

4

Great,

Thanks for the suggestions!