finding a function from observed values

Suppose you have a situation with many variables.

And suppose you have values of this situation for any value of time 9or possible a different variable) that you care to choose..

Is it possible for a computer to match a function from its database as being the nearest match to the results as they are added?

And is it feasible that the function that emerged could be used as a close solution to the problem?

I assume that the computer would have a database of all the known (and extrapolated ) functions that had been imagined in mathematical history.

Am I just looking at an absurdly large computer or is it possible that a simplified versin might cope with small tasks?