arXiv Machine Learning August 18, 2026 By Dongzhe Zheng, Christine Allen-Blanchette

Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivarianc

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arXiv:2608. 14556v1 Announce Type: new Abstract: Physical fields on meshes require a separation between topology and geometry: conservation laws are topological and should be exact, while geometry, material response, and anisotropic coupling must be learned from data.

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arXiv Machine Learning

Jun 15

Approximating Whittle-Matern Fields over Discretized Manifolds

arXiv:2606. 13827v1 Announce Type: cross Abstract: Markovian Whittle-Mat\'ern fields have been convergently approximated by discrete Gauss Markov Random Fields (GMRFs) with sparse precision matrices using a Finite Element approximation of the two-parameter family, \[ (\kappa^2 - \Delta)^{\alpha/2} u = \mathcal{W}, \;\; \kappa \in \mathbb{R}, \; \alpha \in \mathbb{N}.

By Srinivas Nambirajan

arXiv Machine Learning

Jun 17

Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds

arXiv:2606. 13827v2 Announce Type: replace-cross Abstract: Markovian Whittle-Mat\'ern fields have been convergently approximated by discrete Gauss Markov Random Fields (GMRFs) with sparse precision matrices using a Finite Element approximation of the two-parameter family, \[ (\kappa^2 - \Delta)^{\alpha/2} u = \mathcal{W}, \;\; \kappa \in \mathbb{R}, \; \alpha \in \mathbb{N}.

By Srinivas Nambirajan

arXiv Computer Vision

4d ago

Minkowski Attractor Networks: Closed-Form Hyperbolic Flows for Visual Representations

arXiv:2609.37817v1 Announce Type: new Abstract: Geometric representation learning predominantly scaffolds representations onto flat Euclidean subspaces or compact product tori ($\mathbb{T}^K$). Howev...

By Zhongping Ji

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arXiv Machine Learning

Jun 2

Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics

arXiv:2605. 00394v3 Announce Type: replace Abstract: We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics' topological structure from its metric structure.

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arXiv AI

Jun 2

Topology-Preserving Neural Operator Learning via Hodge Decomposition

arXiv:2605. 13834v2 Announce Type: replace-cross Abstract: In this paper, we study solution operators of physical field equations on geometric meshes from a function-space perspective.

By Dongzhe Zheng, Tao Zhong, Christine Allen-Blanchette

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arXiv Machine Learning

Sep 10

Beyond Arbitrary Geometry: Topology Generalization In neural PDE Operators

arXiv:2609.05860v1 Announce Type: new Abstract: Neural operators that accept arbitrary meshes are often treated as geometry-general, but unseen domain topology changes both the invariant and decaying...

By Peiyao Chen, Zhouyuan Xu, Jianguo Nie, Jiansheng Fan, Chen Wang

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