Simulation - identify the input parameters that impact the most the output
With my background on Data Analysis and Nonlinear Regression, your question seems to be very general and blurry. I guess what you are looking for is called Sensitivity Analysis in some contexts.

You need to understand that parameters may have different orders of impact on different sub-spaces of variables (and Parameters) space.

You may also want to generate multiple sub-models based on this sub-spaces, so in each sub-model only a few of your parameters have the main effect and the rest could be neglected.

Again you need to make your question a little more detailed. for example tell us why you want to do this analysis. because your final goal totally impacts the solution.