Induction Motor - Reactances and Leakages
By having a motor those model parameter can be measured from a powered motor or by using it as a generator. As motor it must have a variable and known load.  The current, rpm and torque are expressed as equations derived from the model. A series of tests are performed and the model parameters are fitted by choosing those parameter values that imply the closest results for the measured values.

If the motor is only a detailed 3d model including the materials and geometry, the measurements can be done virtually in full physics simulation software. That software is very expensive.

Addendum: Some good induction motor designs have stayed around a very long time. There exists handbooks that have practical design equations for some of those motor designs. The designs allow some amount of variation without causing the equations to lose their usability. 

In terms of electromagnetism those design equations are approximations - ie. computational electromagnetics in a coarse form. They're based on graphical and empirical methods, but still can produce a proper estimate for the equivqlent circuit and the behaviour with a load.

A set of design equations is valid only for one design assuming it's circle of validity has not been exceeded by too large variation.

An example: http://publish.illinois.edu/grainger-ceme/files/2014/06/CEME1109HarleyGeorgiaTech.pdf