预训练几何神经算子可高效提取点云几何特征，支持噪声鲁棒计算。
Transferable Foundation Models for Geometric Tasks on Point Cloud Representations: Geometric Neural Operators
- 基于点云构建可迁移的几何神经算子，学习微分几何隐表示
- 在含噪条件下准确估计曲率、度量等形状属性，支持任意拓扑表面
- 适用于几何偏微分方程求解与曲率驱动形变计算，适合图形与科学计算领域
我们提出用于获取预训练几何神经算子（GNPs）的方法，可作为几何任务的基础模型，用于提取几何特征。这些模型可集成于机器学习和数值方法的数据处理流程中。实验表明，我们的GNPs能够学习点云的微分几何鲁棒隐表示，从而估计度量、曲率及其他与形状相关的特征。我们展示了预训练的GNPs可用于：(i) 在存在噪声的情况下，对任意形状和拓扑的曲面几何属性进行稳健估计；(ii) 在流形上近似求解几何偏微分方程（PDE）；(iii) 求解曲率驱动形变等形状演化方程。代码与权重已开源，可通过geo_neural_op包直接使用，便于在现有及新数据流程中复用。该模型还可作为涉及几何的数值求解器或几何推理方法的组成部分。
原文摘要 · Abstract (English)
We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.
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