This reminds me of functional data analysis, where they favor spline models (avoids Runge's phenomenon and leverage-point issues), and also heavily emphasize th

This reminds me of functional data analysis, where they favor spline models (avoids Runge's phenomenon and leverage-point issues), and also heavily emphasize thinking about and modeling derivatives. The name "functional" also emphasizes the intention to approximate "y = f(x,z....)". Unfortunately, splines generalize extremely poorly to increasing numbers of dimensions. Even partitioning a seven dimensional space into simplices (ie, Delaunay triangulation), and then trying to keep some number of derivatives continuous across the exploding number of faces becomes computationally burdensome.