If you are interested in parametric modelling, where parameters are more sensitive to the given inputs, you than have to use maximum likelihood estimation, expectation maximization or variational Bayesian approaches. For other details more related to your query, I suggest you follow : Chapter Advanced Methods in Neural Networks-Based Sensitivity Analys...

Article NeuralNetTools : Visualization and Analysis Tools for Neural Networks

you can use one of selecting features methods. For example, CARS-PLS, VIP, and VIF may be useful to select the significant parameters which affect more for your target.

Please follow: https://www.analyticsvidhya.com/blog/2016/12/introduction-to-feature-selection-methods-with-an-example-or-how-to-select-the-right-variables/