Alternatives to regression to decide weights in an expression
First, consider normalising your data, inputs and outputs. If it does not do the desired behaviour, you can have different options.

A simple solution is to add some higher order polynomials to the current features for each input pattern and use the simple linear regression. The fact about that is this that you can not be sure what features you would need due to the fact that you can not see your data. Consequently, if you don't find the acceptable answers you want you can use the current features the higher order polynomials that you are going to add to train an MLP.