I am a bit lost on the concept here, and not sure if this functionality is available in the curve fitting toolbox or machine learning toolbox. I have data from experiments (f(x)) that vary as a function of x. These have been collected by varying a parameter 13 times. I have fitted a non-linear curve (power function) to each of these experiments, and are labelled f(1) to f(13) on the image. Each of these curves share the same independent variable (x), and I am trying to fit the trend of all of these curves into a single function to show how they vary as a function of another parameter (experimental parameter). This creates a multivariable composite function g(f(x),x). Is there any way for me to use an optimization technique in order to fit all of these functions into a single function that show the trend of the curves as I go from 1 to 13? I am quite lost here.
Thank you for any assistance!