English(EN) Topology-Preserving Neural Operator Learning via Hodge Decomposition

新方法使用霍奇分解实现拓扑保持神经算子

作者 PulseAugur 编辑部 · [1 个来源] · 2026-05-13 17:56

研究人员开发了一种在几何网格上学习物理场方程解算子（solution operators）的新方法。他们的方法称为霍奇谱对偶（Hodge Spectral Duality, HSD），利用霍奇分解将可学习的几何动力学与不可学习的拓扑自由度分离开来。这产生了一个混合欧拉-拉格朗日（Hybrid Eulerian-Lagrangian）架构，该架构在保持物理不变量的同时，展现出卓越的准确性和效率。 AI

影响引入了一个新颖的数学框架，用于提高物理模拟中神经算子的准确性和效率。

排序理由该集群包含一篇详细介绍神经算子学习新方法的论文。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.AI TIER_1 English(EN) · Christine Allen-Blanchette · 2026-05-13 17:56

通过霍奇分解实现拓扑保持的神经算子学习

In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective. We reveal that Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geo…

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通过霍奇分解实现拓扑保持的神经算子学习

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