Data modeling techniques for multiple input and multiple output continuous data values?

I am looking for some machine learning techniques/algorithms/functions with the following capabilities:

- can be called as an api from c++

- can model multiple numerical outputs for calibration modeling*

• For example, I have an industrial process which fabricates a high precision component (numerically controlled machine) which has two inputs (temperature, tension) and two outputs (friction, radius), all of which are continuous numerical values. So, for a diversity of input configurations, I want to model what the outputs will be.

Also, I would like to model the reverse, that is, given some output values (friction, radius), I would like to know what the input values should be to obtain those output values.