arXiv:2605. 26854v2 Announce Type: replace Abstract: The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis.
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 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.
arXiv:2606. 19251v1 Announce Type: cross Abstract: Solving the pressure-Poisson equation remains the primary computational bottleneck in incompressible unstructured flow solvers primarily due to the inherent sensitivity of traditional linear solvers to mesh irregularities.
arXiv:2601. 20174v3 Announce Type: replace-cross Abstract: Solving large-scale sparse linear systems originating from partial differential equations (PDEs) is a fundamental topic in high-performance scientific computing, where preconditioners are crucial.
The paper introduces AMELS, an Algebraic Multigrid Acceleration framework for label spreading that speeds up the construction of neighborhood graphs and replaces the standard random walk iteration with an algebraic multigrid solver. By leveraging the multilevel nature of multigrid, AMELS can propagate label information across graphs of any size in a single cycle, achieving substantial runtime reductions and improved robustness to hyperparameter choices. The method enables efficient and accurate label spreading on large‑scale image datasets even when only a few labeled samples are available.
arXiv:2608.27883v1 Announce Type: new Abstract: Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical sta...
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.