arXiv:2606. 05581v1 Announce Type: cross Abstract: Intrinsic methods fill the default toolbox for geometry processing on meshes.
By Arman Maesumi, Tanish Makadia, Aruna Anderson, Oras Phongpanangam, Justin Solomon, Daniel Ritchie
The paper introduces Spectrally Optimised Neural Discretisations (SpeND), a mesh‑free framework that learns discretisation weights from local stencil geometry on unstructured point clouds. By embedding discrete moment conditions into the network architecture, SpeND guarantees polynomial consistency and allows the weights to be optimised for spectral accuracy over a chosen wavenumber band, using an unsupervised Fourier‑mode loss. The resulting operators are PDE‑agnostic, perform well on Poisson, Burgers, and Navier–Stokes equations, and can reduce wall‑clock time by 3–20× compared to existing mesh‑free methods at the same accuracy.
By Lucas Gerken Starepravo, Henry Broadley, Steven Lind, Jack R. C. King
TokenMatch is a transformer-based model that estimates 3D shape correspondences by adaptively tokenising meshes into curvature-guided patches. Trained only on the BeCoS partial-to-partial dataset, it generalises to full-shape matching without retraining, using self‑ and cross‑attention to learn patch‑ and point‑level relations. Evaluated on CP2P, PSMAL, BeCoS, FAUST, SCAPE, and SHREC'19, TokenMatch consistently outperforms existing methods in mean geodesic error and intersection‑over‑union while achieving sub‑second inference speeds.
By Adeela Islam, Zorah L\"ahner, Vittorio Murino, Vladislav Golyanik
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:2609.14841v1 Announce Type: new
Abstract: Scientific machine learning methods such as physics-informed neural networks (PINNs) increasingly rely on domain decomposition for better scalability w...
By Sidharth S. Menon, Irina Tezaur, Ameya D. Jagtap
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
By Marios Koulakis, Constantin Seibold