Geometric Neural Operators (GNPs) for Data-Driven Deep Learning of Non-Euclidean Operators

arXiv:2404.10843v1 Announce Type: cross
Abstract: We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approximate Partial Differential Equations (PDEs) on manifolds, (iii) learn solution maps for Laplace-Beltrami (LB) operators, and (iv) to solve Bayesian inverse problems for identifying manifold shapes. The methods allow for handling geometries of general shape including point-cloud representations. …

abstract accounting arxiv cs.ai cs.lg data data-driven deep learning differential math.oc non-euclidean operators show stat.ml type