No, it can be shown mathematically (and I have posted proofs before) that given any finite set of finitely-represented points, that there are an uncountable infinity of functions that mathematically pass exactly through all of those points.
Because there is an infinite number of potential equations to choose from, the probability that any one equation is the "right" equation is 1/infinity ... which is zero.
The best you can do is pre-determine a finite list of models that have no more parameters than the number of points you have, and do fitting to determine the best model parameters for each possibility, and then check to see which of the models had the "best" fit.
However, it is common to discover that if you do tests by generating points according to a known model and then add even a tiny amount of noise, that some other completely "wrong" model will fit the points better than the known right model form does. For example you might discover that where your actual model was polynomial degree 6 plus a small bit of noise, that a sum-of-exponentials fit better than polyfit(x,y,6)... because by accident there was a small bit of long-term correlation in the noise that was added.
