I would like to apologize upfront for not using accurate/correct terms when I'm describing the following problem.
Suppose I have the following system that I'd like to be able to either accurately sample in efficient time (non-exhaustive sampling) or be able to predict with tolerable error margin. The system has a dependent $Y$ and independent $X,Z,M,I$, $\ Y$ represents energy of some value and the other variables have varying effect on $Y$'s value however let's assume it's strongly linked to $X$ more than the others.
The problem here represents 60% cases where the correlation is inversely proportional and some 40% where it appears as in the image below.
I have tried multiple methods so far to be able to either find improved state through Evolution algorithms/Hill climbing and random search, also have tried linear regression which produced large margin errors when used to predict new dataset. Is there method that would either allow me to construct a model to be used with prediction or simply optimize the problem with minimal time.
