arXiv AI By Alexis de Villeroch\'e, Beniamin Bogosel, St\'ephane Breuils, Dorin Bucur, Jacques-Olivier Lachaud

Neural networks for spectral optimization

Read the original on arXiv AI →

The Flow has not summarised this story yet — read it at arXiv AI.

arXiv Machine Learning
2d ago

Learning Spectrally Optimised Mesh-Free Discretisations

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
arXiv Machine Learning
Aug 11

The Spectral Neuron

arXiv:2608. 08003v1 Announce Type: cross Abstract: As machine learned models increase in complexity and expressive power, features of simpler models, such as interpretability and control over the shape of the modeled function are lost.

By Alex Shtoff
arXiv AI
Jul 7

Learning to Discover Iterative Spectral Algorithms

arXiv:2602. 09530v2 Announce Type: replace-cross Abstract: We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization.

By Zihang Liu, Oleg Balabanov, Yaoqing Yang, Michael W. Mahoney