arXiv：cs.LG· Zhongyan Ouyang, Weixin Liao, Mingquan Feng, Yehui Tang, Junchi Yan·· 3 小时前AI 评分31
Gate-RINS：面向大型稀疏线性系统的残差图像神经子空间求解器
RINS: Residual-Image Neural Subspace Solvers for Large Sparse Linear Systems
AI 导读
研究者提出 Gate-RINS，一种从缓存残差探针生成多项式修正基、并用轻量级逐点门控调制的神经子空间求解器，投影最小二乘更新保持不变，神经组件仅选择扩展方向。在六个 PDE 衍生基准任务和两种规模下，Gate-RINS 在同步墙钟时间内多数设置比 GMRES 和近期纯图神经基线更快达到固定相对残差阈值，混合控制器调度进一步改善残差轨迹。
正文
Abstract:Large sparse linear systems from PDE discretizations require correction subspaces whose operator images explain the current residual. We study this residual-image viewpoint and propose Gate-RINS, a neural subspace solver that generates polynomial correction bases from cached residual probes and modulates them with a lightweight residual- and coordinate-dependent pointwise gate. The projected least-squares update remains unchanged, so the neural component only chooses the expansion directions while the numerical closure tests them through \(\operatorname{range}(AQ_t)\). We also introduce a hybrid controller schedule that composes GRANS-style graph controllers with Gate-RINS under the same projected solver. Across six PDE-derived benchmark tasks and two scales, Gate-RINS reaches fixed relative-residual thresholds faster in synchronized wall-clock time than GMRES and a recent graph-only neural baseline in most settings, and hybrid schedules further improve the residual trajectory. Difficult-mode diagnostics and trajectory visualizations support the interpretation that these gains are associated with operator-image subspaces that align more effectively with the current residual.
| Subjects: | Computational Engineering, Finance, and Science (cs.CE); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.02217 [cs.CE] |
| (or arXiv:2610.02217v1 [cs.CE] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02217 arXiv-issued DOI via DataCite |
Submission history
From: Zhongyan Ouyang [view email]
[v1]
Wed, 9 Sep 2026 08:53:53 UTC (745 KB)
来源：arXiv：cs.LG · arxiv.org