arXiv Machine Learning By Zechen Zhang, Rui Peng Li, Yousef Saad

Graph Neural Multilevel Preconditioners for Iterative Solvers

Read the original on arXiv Machine Learning →

arXiv:2607. 28456v1 Announce Type: cross Abstract: Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning.

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arXiv Machine Learning
Sep 25

A Neural Hierarchical-Matrix Preconditioner for Real-Time GPU Solves

The paper presents a neural hierarchical‑matrix preconditioner designed for real‑time GPU solves of sparse symmetric positive‑definite systems that change each frame. By training a graph‑and‑attention network to predict an SPD approximate inverse in H²‑matrix format, the method achieves linear‑time inference and application, outperforming traditional multigrid setup times and local preconditioners. Experiments on 3D mesh diffusion problems show the preconditioner reduces conjugate‑gradient iterations from 116 to 33 and enables 120 fps real‑time performance for up to 3,647 unknowns.

By Carl Osborne, Minghao Guo, Crystal Owens, Wojciech Matusik
arXiv Machine Learning
Jul 21

One-shot acceleration of transient PDE solvers via online-learned preconditioners

arXiv:2509. 08765v4 Announce Type: replace-cross Abstract: Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.

By Mikhail Khodak, Min Ki Jung, Brian Wynne, Edmond Chow, Egemen Kolemen