arXiv AI July 9, 2026 By Alexandre Quemy

Intrinsic Green's Learning: Supervised Learning on Manifolds via Inverse PDE

arXiv:2607. 07034v1 Announce Type: cross Abstract: We introduce Intrinsic Green's Learning (IGL), a framework that models a target function on a manifold as the solution to a linear PDE whose source term is learned from data.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

arXiv AI

Jun 3

EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs

arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.

By Sungwon Kim, Juho Song, Seungmin Shin, Guimok Cho, Sangkook Kim, Chanyoung Park

arXiv Machine Learning

Sep 7

Nested Inductive Bias Framework for SPD Manifold Learning

The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.

By Tushar Das

rag benchmarks safety

arXiv Machine Learning

Aug 13

Kernel Methods for Learning Operators with Multiple Inputs and Outputs

arXiv:2608. 11831v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning.

By Adrien Weihs, Chunyang Liao, Jingmin Sun, Hayden Schaeffer

benchmarks

arXiv Machine Learning

Sep 1

Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains

arXiv:2608.29892v1 Announce Type: new Abstract: Learning solution operators for partial differential equations (PDEs) on irregular and geometry-dependent domains remains a central challenge in scient...

By Abdolmehdi Behroozi, Chaopeng Shen

rag benchmarks

arXiv AI

4d ago

Building Transformation Layers for Riemannian Neural Networks

arXiv:2609.35436v2 Announce Type: replace Abstract: Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications....

By Ziheng Chen

arXiv Machine Learning

Jun 16

The Data Manifold under the Microscope

arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.

By Marios Koulakis, Constantin Seibold

benchmarks

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Related stories

EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs

Nested Inductive Bias Framework for SPD Manifold Learning

Kernel Methods for Learning Operators with Multiple Inputs and Outputs

Joint Spatiotemporal Spectral Neural Operators for Learning PDEs on Irregular Domains

Building Transformation Layers for Riemannian Neural Networks

The Data Manifold under the Microscope