Approximating Whittle-Matern Fields over Discretized Manifolds

Researchers have developed a new method to approximate Whittle-Matern fields over discretized manifolds using a convergent GMRF approximation, allowing for a universal approximation scheme for precision and covariance matrices.

The method, described in a paper submitted to arXiv on 11 Jun 2026^[1], is agnostic to parameters α and κ, enabling inference rather than guessing. It inherently models pointwise and piecewise-smoothed measurements of a random field, approximating both equally well. The researchers used Discrete Exterior Calculus (DEC) to approximate the fields^[1]. The precision matrices are spectral functions of a graph-laplacian on well-connected and volume-concentrated discretizations. A low rank approximator to the family of such Matérn GMRFs has been provided, which can reduce the number of measurements needed to model the GMRF by compressed-sensing^[1]. The method is computationally independent of the interpolants used, suffering no overhead if one convergent interpolant were replaced with another suitable interpolant over the same mesh^[1]. Another source corroborates the submission of the research paper in 2026^[2].