I am trying to interpolate between points in multiple (eg 6, could be 8 or more) dimensions in Python. I also need to incorporate second derivatives (Hessian) into the interpolation. Derivatives can be incorporated using scipy.interpolate.BPoly.from_derivatives, but this only allows interpolation along x-y pairs in 2D. Further scipy.interpolate.interpn allows higher dimensions but not including second derivatives. Is anyone aware of another regime I could be using here? My only option so far seems to be Taylor expansion around the points and then finding intersecting lines, but that's a bit of a pain in higher dimensions. Can I perhaps do BPoly.from.derivatives for each dimension individually and then bring the information together somehow? Intuition says no but maybe I'm wrong?
Any help greatly appreciated!