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combining FindFit and ParametricNDSolve?


Hello All,
I'd like to use FindFit to find best fit parameter values for a system of differential equations, but instead of  using NDSolve (as is shown in the Help example), I think I need to use ParametricNDSolve to simultaneously fit to multiple datasets that resulted from varying just a single model parameter.  The data is in the form of

{{t1_dataset1, param1, y1_dataset1}, {t2_dataset1, param1_dataset1, y2_dataset1}, ...
{t1_dataset2, param2, y1_dataset2}, {t2_dataset2, param2, y2_dataset2}, ...
{t1_dataset3, param3, y1_dataset3}, {t2_dataset3, param3, y2_dataset3}, ... };

I'm getting very lost in the syntax.  Can anyone give a simple example of how this might be done?
Thanks



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