{"id":"cc709c55-8084-43e3-b7e9-ba07df74114c","arxiv_id":"2607.05934","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.5,"correctness_risk":"unknown","formal_verification":"none","parameter_count":3,"one_line_summary":"FlexRC reduces many-port RC networks via elimination plus a modified block rational Arnoldi process into sparse banded models with user-chosen frequencies and optional port reduction.","lead":"FlexRC is a flexible multi-point model-order reduction method that shrinks large many-port RC circuit networks into smaller sparse models for faster post-layout simulation. Chip designers may care because it targets industrial RC and power-grid nets with tunable accuracy, size, and sparsity.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Passivity and the conservative port-reduction error bound are the hinge of the accuracy claim; if perturbations are not structure-preserving, industrial/IBM transient results may not be underwritten by the analysis.","rationale":"The reader correctly isolated the port-reduction perturbations as the weakest assumption linking the algorithmic knobs to usable transient accuracy and passivity. Full-text scrutiny does not remove that hinge: the method starts from the same elimination as prior high-accuracy work, then adds a nonorthogonal multi-point Arnoldi basis and an optional sparsity control—both of which are secondary once the internal port reduction has already altered the subsystem. Moment matching can hold for the projected system at the chosen expansion points even if passivity is only approximate; the experiments can still look good if tolerances are tight. The load-bearing question is therefore not novelty of the Arnoldi modification or the three user knobs, but whether the perturbations remain small enough (and structured enough) that the discussed passivity properties and the conservative error estimate actually underwrite the industrial and IBM results. That is an empirical/analytic check, not a circularity or consensus issue. Because the reader already marked UNVERDICTED (abstract-only, no code, unreproduced baselines) and this concern does not introduce a new internal contradiction that would force REJECT, the verdict stays UNVERDICTED/UNCHANGED pending the concrete eigenvalue-and-error-estimate check above. Agreement with the reader is full on the identity of the soft spot; the stress pass only sharpens it into a falsifiable matrix-level test.","tokens_in":2072,"tokens_out":739,"duration_ms":31184,"concrete_test":"On the largest IBM power-grid case at the paper’s stated port-reduction tolerance: (1) form the final reduced G_r, C_r and check min eigenvalues of their symmetric parts (or the standard RC descriptor passivity LMIs); (2) compare the paper’s conservative port-reduction error estimate to the actual max relative transient error vs a fine reference. If any eigenvalue is negative, or the estimate under-predicts true transient error by more than ~2×, the passivity/error support for the central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that FlexRC’s elimination-plus-modified-block-rational-Arnoldi pipeline, with tolerance-controlled internal port reduction, yields sparse banded ROMs that are faster to build and to simulate in transient than prior elimination-based methods while remaining accurate. That claim rests on the port-reduction step applied to the internal subsystem after the shared elimination. Congruence with any full-rank basis preserves PSD of G and C, so exact RC passivity would survive a pure projection; the paper instead applies “port-reduction perturbations” and only discusses passivity under those perturbations, plus a conservative error estimate. If those perturbations are structural (e.g., dropping weak internal couplings, approximate Schur reduction of internal ports, or non-congruence truncation controlled by a tolerance), they can destroy exact PSD or make the error estimate fail to control true transient error. The industrial RC and IBM power-grid experiments then become the only evidence that the reduced models stay usable; the analysis no longer guarantees it. This is the single load-bearing soft spot: without a structure-preserving (or rigorously bounded) port-reduction step, the multi-point flexibility and sparsity knobs do not by themselves secure the accuracy/passivity needed for the effectiveness claim.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript proposes FlexRC, a multi-point model-order reduction method for many-port RC networks. After an elimination step shared with prior high-accuracy methods, it builds a nonorthogonal projection basis via a modified block rational Arnoldi process to obtain sparse banded reduced-order models. The method exposes three user controls: selectable expansion frequencies, a tolerance-driven port-reduction step on the internal subsystem, and an optional sparsity-control strategy. The authors supply a moment-matching analysis, a discussion of passivity under the port-reduction perturbations, and a conservative error estimate for that port reduction. Numerical experiments on industrial RC nets and IBM power-grid benchmarks are used to argue improved reduction time and transient simulation time relative to existing elimination-based techniques.","tokens_in":2300,"tokens_out":1302,"duration_ms":26948,"significance":"If the analysis and experiments hold, FlexRC would address genuine practical limitations of current elimination-based RC MOR: fixed expansion points, oversized ROMs, and high reduction cost for many-port nets that arise in post-layout simulation. The combination of multi-point flexibility, tolerance-controlled internal port reduction, and optional sparsity control is of clear engineering interest, and the inclusion of moment-matching analysis plus an a-priori port-reduction error estimate is a methodological strength relative to purely heuristic sparsification. Successful, structure-aware reduction of industrial and IBM power-grid RC networks would be a useful contribution to the circuit-simulation community.","major_comments":[{"comment":"The central accuracy/passivity claim rests on the tolerance-controlled port-reduction step applied to the internal subsystem after elimination. Congruence with a full-rank basis would preserve positive-semidefiniteness of the conductance and capacitance matrices; the manuscript instead applies 'port-reduction perturbations' and only discusses passivity under those perturbations. The report must make explicit whether those perturbations are structure-preserving (e.g., a congruence or a Schur reduction that retains PSD) or are approximate truncations/droppings of weak couplings. If the latter, exact RC passivity is lost and the subsequent transient claims are no longer underwritten by the congruence argument alone. A precise statement of the perturbation operator and a proof (or counter-example) of PSD retention are load-bearing for the effectiveness claim.","section":"passivity discussion / port-reduction technique"},{"comment":"The 'conservative error estimate for port reduction' is cited as supporting accuracy of the reduced models used in transient simulation. The manuscript should state the precise norm and the quantity being bounded (transfer-function residual, state trajectory, port voltages/currents), show that the estimate is independent of the subsequent multi-point projection (or quantify the interaction), and demonstrate on at least one industrial/IBM example that the a-priori bound actually majorizes the observed transient or frequency-response error. Without that comparison, the estimate remains formal and does not underwrite the numerical effectiveness claim.","section":"error estimate for port reduction; numerical experiments"},{"comment":"Moment-matching analysis is asserted for the modified block rational Arnoldi basis. Because the basis is nonorthogonal and is applied after a perturbed internal subsystem, the standard block-rational Krylov moment-matching argument does not apply verbatim. The manuscript should state which moments (at which expansion points, of which transfer function—original, eliminated, or port-reduced) are matched exactly, and whether matching is lost under the port-reduction perturbations. A short lemma with the precise matching order would make the multi-point claim rigorous rather than heuristic.","section":"moment-matching analysis; modified block rational Arnoldi"},{"comment":"The experimental claim of superior reduction time and transient simulation time versus 'existing elimination-based methods' needs a controlled comparison: same expansion points (or a fair multi-point baseline), same error tolerance, same sparsity target, and reporting of both offline reduction cost and online transient cost on identical industrial RC and IBM power-grid instances. If the baselines are single-point or do not exploit port reduction, the speed-up may be attributable to the extra knobs rather than to the algorithmic core. Tables that isolate the contribution of each of the three adjustable components would make the effectiveness claim attributable.","section":"numerical experiments on industrial RC and IBM power-grid examples"}],"minor_comments":[{"comment":"Define the precise meaning of 'sparse banded' for the reduced model (bandwidth as a function of number of expansion points and block size) early, so that the optional sparsity-control strategy can be compared against the default banded structure.","section":"method overview / reduced-model structure"},{"comment":"Clarify the relationship between the user-specified frequency points and the modified block rational Arnoldi shifts: whether shifts are exactly the user frequencies, how repeated shifts are handled, and how the block size is chosen for many-port inputs.","section":"modified block rational Arnoldi process"},{"comment":"State the units and normalization of the port-reduction tolerance so that the reported tolerance values in the experiments are reproducible by other groups.","section":"tolerance-controlled port-reduction; experimental setup"},{"comment":"If the optional sparsity-control strategy can destroy the banded pattern or the moment-matching property, note the trade-off explicitly when the option is introduced.","section":"optional sparsity-control strategy"}],"recommendation":"major_revision","confidential_remarks":"The abstract and the stress-test note correctly identify passivity-under-perturbation and the port-reduction error estimate as the hinge of the paper. I have not treated 'outside consensus' as a defect; the concern is internal: whether the perturbations remain compatible with the PSD/passivity and error arguments that the effectiveness claim needs. If the authors can supply a structure-preserving formulation (or a tight, validated bound) and a controlled experimental isolation of each knob, the contribution is publishable. Scope fit for eess.SY / circuit-simulation MOR is appropriate."},"author_rebuttal":{"model":"grok-4.5","summary":"We thank the referee for a careful and constructive report. The four major comments correctly identify places where the manuscript’s claims on passivity, the port-reduction error estimate, moment matching after the modified Arnoldi step, and the experimental attribution of speed-ups need to be stated more precisely and supported more carefully. We agree with the substance of each point and will revise the paper accordingly: we will give an explicit definition of the port-reduction operator and a clear PSD analysis, tighten the statement of the a-priori error bound and add a numerical majorization check, supply a short lemma that states exactly which moments of which transfer function are matched (and under which conditions matching is retained), and restructure the experimental section so that the contribution of each of the three adjustable components is isolated under controlled baselines. None of these revisions changes the algorithmic core of FlexRC; they make the existing analysis and numerical claims rigorous and attributable. Detailed point-by-point replies follow.","responses":[{"response":"We agree that the present discussion is not sufficiently precise and that the nature of the port-reduction operator is load-bearing. In the revised manuscript we will (i) define the port-reduction operator explicitly as a tolerance-driven truncation of weak internal couplings after the elimination step (i.e., an approximate dropping, not a pure congruence or exact Schur reduction on the retained ports), (ii) state clearly that exact positive-semidefiniteness of the conductance/capacitance blocks is therefore not automatically inherited from congruence, and (iii) replace the informal passivity discussion by a short analysis that bounds the size of the symmetric part of the perturbation and gives conditions under which the perturbed internal matrices remain positive semidefinite (or, when they do not, how a simple diagonal compensation restores PSD while preserving the same first-order error level). We will also note that the subsequent multi-point projection is still a congruence, so any residual passivity violation can only originate from the port-reduction step itself. These changes make the passivity claim accurate rather than overstated; the numerical effectiveness claims will then rest on the controlled error estimate (see next point) rather than on an unqualified congruence argument.","revision_made":"yes","referee_comment":"The central accuracy/passivity claim rests on the tolerance-controlled port-reduction step applied to the internal subsystem after elimination. Congruence with a full-rank basis would preserve positive-semidefiniteness of the conductance and capacitance matrices; the manuscript instead applies 'port-reduction perturbations' and only discusses passivity under those perturbations. The report must make explicit whether those perturbations are structure-preserving (e.g., a congruence or a Schur reduction that retains PSD) or are approximate truncations/droppings of weak couplings. If the latter, exact RC passivity is lost and the subsequent transient claims are no longer underwritten by the congruence argument alone. A precise statement of the perturbation operator and a proof (or counter-example) of PSD retention are load-bearing for the effectiveness claim."},{"response":"The referee is correct that the current estimate is stated too loosely to underwrite the numerical claims. In the revision we will: (1) specify that the bound is an a-priori estimate on the H2 (or induced L2) residual of the port-to-port transfer function of the internal subsystem after elimination, measured in the Frobenius norm of the discarded coupling blocks scaled by the chosen tolerance; (2) prove that the bound depends only on the eliminated/port-reduced system and is therefore independent of the subsequent multi-point Arnoldi projection (the projection error is controlled separately by the usual residual of the rational Krylov process); and (3) add a dedicated numerical check on at least one industrial RC net and one IBM power-grid instance that plots the a-priori bound against the observed frequency-response and transient port-voltage errors, confirming that the bound majorizes the measured error. Where the bound is conservative we will say so explicitly. These additions turn the estimate from a formal remark into a verifiable accuracy certificate for the port-reduction step used in the experiments.","revision_made":"yes","referee_comment":"The 'conservative error estimate for port reduction' is cited as supporting accuracy of the reduced models used in transient simulation. The manuscript should state the precise norm and the quantity being bounded (transfer-function residual, state trajectory, port voltages/currents), show that the estimate is independent of the subsequent multi-point projection (or quantify the interaction), and demonstrate on at least one industrial/IBM example that the a-priori bound actually majorizes the observed transient or frequency-response error. Without that comparison, the estimate remains formal and does not underwrite the numerical effectiveness claim."},{"response":"We accept this criticism. The present text asserts moment matching without isolating the effect of nonorthogonality and of the port-reduction perturbation. The revised manuscript will contain a short lemma that states: (a) in the absence of port reduction, the modified block rational Arnoldi basis (even though nonorthogonal) still produces a reduced model that matches the block moments of the eliminated system’s transfer function at each user-chosen expansion point up to the order determined by the number of Arnoldi steps per point; (b) when the tolerance-controlled port-reduction is applied first, exact moment matching holds for the port-reduced (perturbed) transfer function, while the moments of the original/eliminated transfer function are matched only up to an additive residual controlled by the same port-reduction tolerance that appears in the error estimate; (c) the matching statement is therefore with respect to the system that is actually projected, and any loss of matching relative to the unperturbed system is quantified rather than ignored. The proof follows the standard block-rational Krylov argument once the nonorthogonal basis is written in the appropriate oblique-projection form; we will include the short derivation. This makes the multi-point claim rigorous.","revision_made":"yes","referee_comment":"Moment-matching analysis is asserted for the modified block rational Arnoldi basis. Because the basis is nonorthogonal and is applied after a perturbed internal subsystem, the standard block-rational Krylov moment-matching argument does not apply verbatim. The manuscript should state which moments (at which expansion points, of which transfer function—original, eliminated, or port-reduced) are matched exactly, and whether matching is lost under the port-reduction perturbations. A short lemma with the precise matching order would make the multi-point claim rigorous rather than heuristic."},{"response":"We agree that the current experimental section does not fully isolate the three adjustable components and that some of the reported speed-ups could be attributed to the extra knobs rather than to the algorithmic core alone. In the revision we will restructure the numerical section as follows. (1) All methods will be run on the same industrial RC and IBM power-grid instances, with identical error tolerances and, where applicable, the same sparsity target. (2) We will include a fair multi-point baseline (elimination followed by a standard multi-point block rational Arnoldi without our port-reduction or sparsity-control steps) so that the benefit of the modified process itself is visible. (3) We will add ablation-style tables that turn on, one at a time, (i) user-chosen multi-point expansions, (ii) tolerance-controlled internal port reduction, and (iii) the optional sparsity-control strategy, reporting offline reduction time, ROM size/sparsity, and online transient simulation time for each configuration. (4) Single-point elimination-based methods will remain as reference points, but will no longer be the sole baseline. These changes make the effectiveness claim attributable to each component and remove the ambiguity the referee correctly identified.","revision_made":"yes","referee_comment":"The experimental claim of superior reduction time and transient simulation time versus 'existing elimination-based methods' needs a controlled comparison: same expansion points (or a fair multi-point baseline), same error tolerance, same sparsity target, and reporting of both offline reduction cost and online transient cost on identical industrial RC and IBM power-grid instances. If the baselines are single-point or do not exploit port reduction, the speed-up may be attributable to the extra knobs rather than to the algorithmic core. Tables that isolate the contribution of each of the three adjustable components would make the effectiveness claim attributable."}],"tokens_in":2007,"tokens_out":1785,"duration_ms":22559,"standing_objections":[]},"desk_editor":{"model":"grok-4.5","letter":"The one thing to know is that FlexRC is not a new theory of MOR. It starts from the same elimination step used by prior high-accuracy RC methods, then builds a nonorthogonal multi-point basis via a modified block rational Arnoldi process, and adds tolerance-controlled internal port reduction plus optional sparsity control. The reduced models are sparse and banded, with three user knobs: frequency points, port-reduction tolerance, and sparsity strategy. That package, plus the supporting analysis and industrial/IBM experiments, is the contribution.\n\nWhat it does well is address real pain points of elimination-based RC reduction: fixed frequencies, oversized ROMs, and high reduction cost. Moment matching is analyzed, they give a conservative error estimate for the port-reduction step, and they discuss passivity under the perturbations that step introduces. The experiments claim better reduction time and transient simulation time on industrial RC nets and IBM power grids. For post-layout and power-grid verification that is useful progress, not theater.\n\nThe soft spot is the one the stress-test flags, and it is load-bearing but not automatically fatal. Exact RC passivity (PSD of G and C) survives congruence with a full-rank basis. FlexRC instead applies port-reduction perturbations to the internal subsystem and only discusses passivity under those perturbations. If those steps drop weak couplings, do approximate Schur reduction, or otherwise break structure, the analysis no longer guarantees the accuracy/passivity the effectiveness claim needs; the industrial and IBM transient numbers become the main evidence. A referee should pressure the equations, the error bound tightness, and the tables. That is a real hinge, not a manufactured flaw. Free parameters are intentional user knobs, not fitted constants. No circular derivation shows up from the abstract and method framing.\n\nWho this is for: people who reduce many-port post-layout RC and power-grid networks and care about wall-clock reduction and transient cost. A serious EDA/MOR referee should see it. I would not desk-reject. Bring it to reading group only if someone is actively doing RC MOR; otherwise skip. I would not cite it in my own work unless I start working that problem.","headline":"FlexRC is a practical multi-point elimination-plus-Arnoldi package for many-port RC MOR; the port-reduction passivity/error story is the real hinge, but the paper still deserves a serious referee.","tokens_in":2966,"tokens_out":551,"would_cite":false,"duration_ms":20466,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"FlexRC builds sparse multi-point reduced models for many-port RC nets that cut reduction and transient sim time","keywords":["model order reduction","RC networks","many-port systems","block rational Arnoldi","passivity","moment matching","power grid","circuit simulation"],"falsifier":"On a standard industrial RC or IBM power-grid net, measure whether the FlexRC reduced model (with a given port-reduction tolerance) either loses passivity, exceeds the stated conservative error bound, or produces larger reduction or transient-simulation times than the elimination-based baselines the paper compares against.","tokens_in":2931,"feed_emoji":"⚡","tokens_out":607,"duration_ms":71961,"temperature":0.7,"pith_summary":"Post-layout circuit simulation needs fast, accurate reduced models of huge resistor-capacitor (RC) networks that have many external ports. Prior high-accuracy elimination methods either lock the expansion frequencies, leave oversized models, or spend too much time on the reduction itself. FlexRC starts from the same sparse elimination of internal nodes, then builds a nonorthogonal projection basis with a modified block rational Arnoldi process so the reduced system stays sparse and banded. The user can pick the expansion frequencies, dial a tolerance that further collapses internal ports, and optionally keep the reduced matrix even sparser. The paper shows that the resulting models match selected moments, remain passive under the controlled port-reduction perturbations, and come with a conservative error bound for that step. On industrial RC nets and IBM power-grid benchmarks the method finishes reduction faster and yields models that simulate faster in the time domain than existing elimination-based competitors.","feed_headline":"Sparse multi-point reduced models speed many-port RC simulation","feed_subtitle":"User-chosen frequencies, tolerance-controlled ports and optional sparsity cut both reduction and transient time","key_machinery":"A modified block rational Arnoldi process that builds a nonorthogonal projection basis after the initial sparse elimination of internal nodes. The basis maps the many-port RC system onto a sparse banded reduced model whose size and structure are controlled by user-selected expansion points, a port-reduction tolerance, and an optional sparsity parameter.","core_discovery":"Starting from the same internal-node elimination used by prior high-accuracy methods, FlexRC constructs a nonorthogonal projection basis via a modified block rational Arnoldi process and thereby produces sparse banded reduced-order models of many-port RC networks. The construction admits user-chosen frequency points, a tolerance-driven reduction of the internal subsystem’s ports, and an optional sparsity-control step, while still guaranteeing moment matching, passivity under the induced perturbations, and a conservative error estimate for the port-reduction stage.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["FlexRC: multi-point projection builds sparse banded ROMs for many-port RC","User-specified frequencies yield sparse multi-point models of many-port RC nets","Tolerance-driven port reduction produces sparse FlexRC models for RC networks","Modified block rational Arnoldi enables flexible sparse MOR for many-port RC","Sparse banded multi-point ROMs cut reduction and simulation time for RC nets"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The port-reduction perturbations applied to the internal subsystem stay small enough that the claimed passivity properties and the conservative error estimate continue to hold on the industrial RC and IBM power-grid examples, so the reduced models remain accurate enough for transient simulation.","fun_headline_variants_meta":{"raw":{"variants":["FlexRC: multi-point projection builds sparse banded ROMs for many-port RC","User-specified frequencies yield sparse multi-point models of many-port RC nets","Tolerance-driven port reduction produces sparse FlexRC models for RC networks","Modified block rational Arnoldi enables flexible sparse MOR for many-port RC","Sparse banded multi-point ROMs cut reduction and simulation time for RC nets"]},"model":"grok-4.5","cost_usd":0.013198,"raw_usage":{"total_tokens":2733,"prompt_tokens":752,"num_sources_used":0,"completion_tokens":105,"cost_in_usd_ticks":131980000,"prompt_tokens_details":{"text_tokens":752,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1876,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":752,"tokens_out":105,"duration_ms":26346,"temperature":1.0,"reasoning_tokens":1876,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-08T19:25:04.228637+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"On a standard industrial RC or IBM power-grid net, measure whether the FlexRC reduced model (with a given port-reduction tolerance) either loses passivity, exceeds the stated conservative error bound, or produces larger reduction or transient-simulation times than the elimination-based baselines the paper compares against.","supporting_citations":[],"review_version":1}