Overview
Overview: The GeoNeuralOp package provides methods for deep learning with point-cloud manifold representations. This includes geometric approaches for learning differential operators, extracting features, shape deformations, and other tasks.
Features:
Curvature and Metric Estimators: Operator training methods for obtaining approximations of local curvatures, metrics, and geometric differential operators on point-clouds.
PDE Neural Solvers: Data-driven numerical methods for geometric PDEs on manifolds, such as Laplace-Beltrami and other problems.
Dynamic Shape Deformations: Shape evolution of point-clouds, such as mean-curvature driven-flows.
Transferable Pretrained Models: Provides weights for models for use in existing data processing pipelines for estimating local curvatures, Laplace-Beltrami operators, components for PDE solvers, and other geometric tasks.
The package also includes variants of GNPs for efficient training based on factorizations and other protocols. For more details and pretrained models see the papers and examples below.
Please cite for this package:
Geometric neural operators (gnps) for data-driven deep learning in non-euclidean settings, B. Quackenbush, P.J. Atzberger, Machine Learning: Science and Technology, 5(4), (2024), https://doi.org/10.1088/2632-2153/ad8980.
Additional papers:
Transferable Foundation Models for Geometric Tasks on Point Cloud Representations: Geometric Neural Operators, B. Quackenbush, P.J. Atzberger, Machine Learning: Science and Technology, 6(4), (2025), https://doi.org/10.1088/2632-2153/ae1bf8.
Extending Neural Operators: Robust Handling of Functions Beyond the Training Set, B. Quackenbush, P.J. Atzberger, Machine Learning: Science and Technology, 6(4), (2025), https://arxiv.org/abs/2603.03621.
For installation and examples, please see https://github.com/atzberg/geo_neural_op.
Package Reference: