In general, absolutely no. This is impossible. Why do I say that? Consider even an absolutely trivial linear model. I don't need anything fancy here.
z = x + y
Suppose you estimate that model from some data. I've even been lazy, and given you a very simple result, of some hypotheocal model, with a very boring set of coefficients.
Now your goal will be, given a value of z, what are the values of x and y? For example, z == 3. Now, what were the original values of x and y? It might have been any of (x,y) = (1,2), of (2,1), or (1.5,1.5), or (-7000234,7000237), or infinitely many other choices.
Worse, your model will generally be nonlinear. And that means the inverse will very frequently result in multiple branches.
Essentially, anytime you have more inputs than outputs, then there will be no way to identify a unique inverse. At best, you could fix some of the variables at some arbitrary level, and then use a nonlinear solver (like fsolve) to solve for a solution for the rest of the variables. Even then, there will likely be multiple solutions per my comment above. Or, there may be no solutions at all.
Sorry, but you can't always get what you want. (I'm sure somebody said that before me.)
