English(EN) A Data-Driven Interpolation Method on Smooth Manifolds via Diffusion Processes and Voronoi Tessellations

新的插值方法结合了扩散和Voronoi剖分

作者 PulseAugur 编辑部 · [1 个来源] · 2026-07-14 04:00

研究人员开发了一个新颖的数据驱动插值框架，旨在从散点数据中重建光滑流形上的实值函数。该方法集成了高斯核插值器和Voronoi自适应带宽，带宽由数据的几何形状决定。该方法提供了一个封闭形式的解，无需训练、迭代优化或参数调整，并且可以相对于样本点的数量以线性复杂度高效计算。 AI

影响这项研究引入了一个新的数据插值数学框架，有可能提高各种科学和工程应用中函数重建的准确性和效率。

排序理由该集群包含一篇提交到arXiv的学术论文。[lever_c_demoted from research: ic=1 ai=0.7]

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arXiv cs.LG TIER_1 English(EN) · Alvaro Almeida Gomez · 2026-07-14 04:00

基于扩散过程和Voronoi图的流形上数据驱动插值方法

arXiv:2509.03758v5 Announce Type: replace Abstract: We propose a data-driven interpolation framework for reconstructing real-valued functions on smooth manifolds from scattered pointwise observations. The method combines a Gaussian Nadaraya--Watson kernel interpolant with a Voron…