A Data-Driven Interpolation Method on Smooth Manifolds via Diffusion Processes and Voronoi Tessellations

ArXi:2509.03758v3 Announce Type: replace We propose a data-driven interpolation method for approximating real-valued functions on smooth manifolds, based on the Laplace--Beltrami operator and Voronoi tessellations. Given pointwise evaluations of a function, the method constructs a continuous extension over the manifold by exploiting diffusion processes and the intrinsic geometry of the data. The proposed approach is entirely data-driven and requires neither a