PSI: Constructing ad-hoc Simplices to Interpolate High-Dimensional Unstructured Data

Abstract

Interpolating unstructured data using barycentric coordinates becomes infeasible at high dimensions due to the prohibitive memory requirements of building a Delaunay triangulation. We present a new algorithm to construct ad-hoc simplices that are empirically guaranteed to contain the target coordinates, based on a nearest neighbor heuristic and an iterative dimensionality reduction through projection. We use these simplices to interpolate the astrophysical cooling function $\Lambda$ and show that this new approach produces good results with just a fraction of the previously required memory.