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

TL;DR

This paper introduces a novel algorithm for high-dimensional data interpolation that constructs ad-hoc simplices using a nearest neighbor heuristic and dimensionality reduction, significantly reducing memory usage.

Contribution

It presents a new method for constructing simplices to interpolate high-dimensional unstructured data efficiently, overcoming the limitations of traditional Delaunay triangulation.

Findings

Effective interpolation of astrophysical cooling function $\\Lambda$

Reduces memory requirements compared to existing methods

Produces accurate results in high-dimensional settings

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.