Data-Driven Diffusion Processes on Differential Forms via the Projected Ambient Connection Laplacian

תקציר מקורי באנגליתarXiv:2607.23192v1 Announce Type: cross Abstract: We develop a data-driven approximation of the projected ambient connection Laplacian acting on differential forms over smooth Riemannian manifolds sampled by point clouds. The proposed construction extends the classical framework of diffusion maps and Vector Diffusion Maps from scalar functions and tangent vector fields to differential forms of arbitrary degree. Our approach is based on a novel representation of differential forms as alternating differential arrays obtained through an extension of the classical musical isomorphism. This representation enables the construction of a matrix-valued diffusion operator that approximates the projected ambient connection Laplacian directly from point cloud data without requiring a mesh or simplicia