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

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 $Λ$ and show that this new approach produces good results with just a fraction of the previously required memory.

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