English(EN) Data-Driven Diffusion Processes on Differential Forms via the Projected Ambient Connection Laplacian

新方法近似微分形式上的扩散过程

作者 PulseAugur 编辑部 · [1 个来源] · 2026-07-28 04:00

研究人员开发了一种新颖的数据驱动方法来近似投影环境连接拉普拉斯算子，该算子作用于黎曼流形上的微分形式，而这些流形由点云采样。该方法将现有的扩散图技术扩展到处理任意阶的微分形式，利用了从交替微分数组派生的值矩阵扩散算子。该方法允许为微分形式上的热方程构建显式欧拉格式，并通过在单位球体上的数值实验进行了验证，证实了其有效性。 AI

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在 arXiv cs.LG 阅读 →

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arXiv cs.LG TIER_1 English(EN) · Alvaro Almeida Gomez, Jorge Duque Franco · 2026-07-28 04:00

数据驱动的微分形式上的扩散过程通过投影环境联络拉普拉斯算子实现

arXiv: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 …

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数据驱动的微分形式上的扩散过程通过投影环境联络拉普拉斯算子实现

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