arXiv:2605. 26854v2 Announce Type: replace Abstract: The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis.
By Yali Fink, Ido Ben-Yair, Lars Ruthotto, Eran Treister
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.
By Alexander Benanti, Xi Han, Hong Qin
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.
By Zechen Zhang, Rui Peng Li, Yousef Saad
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:2608. 09921v1 Announce Type: new Abstract: Foundation models are transforming business workflows and boosting productivity, yet they remain largely absent from engineering domains such as power system analysis, where strict physical consistency must be enforced.
By Alban Puech, Matteo Mazzonelli, Tamara R. Govindasamy, Mangaliso Mngomezulu, H\'ector Maeso-Garc\'ia, Thomas Tolhurst, Javad Bayazi, Ali Moeini, Naomi Simumba, Celia Cintas, David Nelischer, Romeo Kienzler, Jonas Weiss, Anna Varbella, Florian D\"orfler, Gabriela Hug, Martin Mevissen, Juan Bernab\'e-Moreno, Fran\c{c}ois Mirall\`es, Hendrik F. Hamann, Etienne Vos, Thomas Brunschwiler
arXiv:2607. 11672v1 Announce Type: new Abstract: Industrial design in fields such as vehicle and aerospace engineering often relies on large-scale numerical simulations to evaluate fluid dynamics performance, which can incur substantial computational costs.
By Li Xiao, Tianyu Li, Yiye Zou, Mingjie Zhang, Xiaogangd Deng