RINS: פתרונות נוירוניים למערכות ליניאריות דלילות

תקציר מקורי באנגליתarXiv:2610.02217v1 Announce Type: cross 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 ta