How to estimate the Rn->Rn function (operator) with effective algorithm

Hi everybody,

I'm doing a blackbox like estimation of a Rn->Rn mapping. I have a few sampling points, which can be regarded as the known knowledge for the supervision learning. My objective is to acquire the interpolation over a bounded range in Rn, which is equivalent as estimating the Rn->Rn blackbox function (operator). I learnt that matlab build in function interpn can only dealt with scalar function, namely, Rn->R1. I wonder, this there any effective algorithm that can be easily customized for such estimation/interpolation. Thanks in advance.

Answer 1

[Matt J]

lsqcurvefit would be worth considering, if you have a differentiable parametric model for the Rn-->Rn mapping.

[Fu-Rui Xiong]

Thanks for the tips. However, the problem at hand remain to be interpolated is just a blackbox structure without certain analytic functional structure (it is a cell mapping like estimation). Anyway, thanks for your kind help. Have a nice day.

[Matt J]

If it's just a question of how to get vector-valued output from interpn, there' no reason you can't call interpn n times, once for each component of the output. In other words, if the mapping is

 y=F(x)=[F_1(x) F_2(x) ... F_n(x)]

you can just evaluate each scalar function F_i(x) by interpn, griddedInterpolant, or scatteredInterpolant, whichever is the most appropriate.