Phd student here. For my thesis I have a problem to solve. I have written an algorithm, which generates a curve for some model (alpha-hemolysin makes spores on cell membrane over time). That model uses like $20$ constants: $k_{01},\dotsc,k_{20}$. Now, what I need to do is make it the other way around: I have a curve (from real experiment data). Now need to find those constants $k_{xx}$, so that the generated curve would best fit the real experiment curve, marked by arrow between blue marks in the image below.
I will probably need to write some function which would return total difference between the generated curve and the real curve and try to minimize it by applying various $k_{xx}$ sets. Would machine learning be suitable for it? Is there any other approach? Any suggestions or hints are very welcome, as I had no experience before and this is very new to me. PS will use Orange as a tool. Thank you!
We can compare the behavior/tendency to a particular case of a well known tan hyperbolic function of given starting slope that goes asymptotically to zero.
Like for example
$$ y= y_{max} \tanh c \cdot x $$ of starting slope
$$ y'= y_{max} \cdot c $$
where $y_{max}$ is the constant steady state asymptotic value it tends to and $c$ is a constant that represents the rate at change at start.
Another example is a trigonometric tangent related function
$$ y= 1-\frac{1}{x}$$
that has such a tendency towards either axis: