No. Sorry, but no. In general it is not possible to come up with a set of "equations" that represent any general relationship. For example, suppose I gave you a set of random numbers? What equation represents those numbers?
If you know a proper model that you expect the relationship to follow, then you can use a linear or nonlinear regression to estimate the parameters for that model. But that requires you to know something about the process, and to have a viable model for that process.
Usually at best you can use an interpolant, so in 3 dimensions, something like interp3 or interpn.
