high-order polynomial surrogates?

[stevengj]

Right now I see that you have linear and 2nd-order polynomials, but it might be nice to support arbitrary order.

In case it is of interest, I have a reasonably fast implementation of arbitrary-order arbitrary-dimensionality Chebyshev interpolation/fitting supporting multiple outputs and differentiation at https://github.com/stevengj/FastChebInterp.jl (currently unregistered). (We originally used https://github.com/RJDennis/ChebyshevApprox.jl, but it wasn't fast enough for our purposes, and ApproxFun.jl isn't aimed at high-dimensional surrogates.)

(It can either do Chebyshev interpolation, for functions sampled at Chebyshev points, or Chebyshev least-square fitting from arbitrary points.)

[ChrisRackauckas]

Agreed this is needed. This repo needs those, but also it needs a bit more optimization work.

[stevengj]

(Note that the FastChebInterp package has been registered for a while now and is pretty stable.)