Use trained non linear regression model to identify variables that maximize the predicted value
For non linear regression are you using SVM Kernel approach or deep learning?  One of the articles I have referred to in the past is this research paper from computational biology where in they have defined a measure for feature importance. I had come across this in the past when preparing for an interview so didnt actually try it out and see if it works.The link to the article :- [https://arxiv.org/pdf/1611.07567.pdf] . Let me know incase you do practically try this out