Geometric Neural Operators (GNPs) for Data-Driven Deep Learning of Non-Euclidean Operators
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Abstract (arXiv)
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. The developed GNPs provide approaches for incorporating the roles of geometry in data-driven learning of operators.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 17 of its 46 references that are in the map. First posted on arXiv 16 Apr 2024.
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17 of 46 references.
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Citing papers per year: 2026: 2.
2 papers.