How do you get from experimental measurements to models?
You question confuses a bunch of things. Yes, there are curve fitting methods that minimize the error. That's what you [or software like MODPEX] use[s] to generate the SPICE parameters that best represent a set of device curves that were measured. But note that the model/equations is/are determined beforehand.

However you need a model that has some theoretical basis before you fit some data to it. There's no cookbook method for coming up with the latter although some things like dimensional analysis help. But dimensional analysis can't tell you if you should have \$(V_1-V_2)\$ or \$\sqrt{V_1^2+V_2^2}\$ in your formula; both are measured in volts. To decide between something like these you need some deeper theoretical basis [which is domain dependent]; and hopefully it agrees with the experimental evidence.

If you're going to have a model that's purely empirical, i.e.
has no theoretical basis and is just based on prior measurements,
you need to understand the risks/uncertainty involved in such a
model, like the distinction between sample and population. See for
example http://arxiv.org/pdf/math/0610849.pdf for more (particularly pp. 103-104).
Probably the best place to ask for more is the https://stats.stackexchange.com/ site. Such
purely empirical models are more common in social sciences.