As I try to process some physic experiment data that I don't have the closed form formula with unknown parameters, I have to use some regression models like polynomials or normal distributions . The problem here is that polynomials can't fit good enough when degree is low and have too many local extreme points when it is too high. And other closed forms have the similar or other problems.
Thus, it got me thinking whether there are methods or tools to just compute the most fitted curves or surface without getting a closed form, like some robust methods. And by only computable, it is used to predict values at certain points.
And by the most fitted, I mean that it has as less local extreme points as possible and do turn if the data has the trend and after all, differentiable or continuous at least.
I try to look up some materials in the google scholar and found nothing that I wanted. I wonder if there are on-going researches or already finished works on this. Thanks