RINS: Residual-Image Neural Subspace Solvers for Large Sparse Linear Systems
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 ...
| Authors | Zhongyan Ouyang, Weixin Liao, Mingquan Feng et al. |
|---|---|
| Primary category | cs.CE |
| Published | 9 September 2026 |
| Last updated at source | 9 September 2026 |
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