{"id":"03675bdb-a3f2-4e1d-bee4-bcde59d253da","arxiv_id":"2605.19536","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Dual HRKAN framework (DPIKAN-TO) for topology optimization with one network predicting displacements and another handling sensitivity-based design updates.","lead":"The paper proposes DPIKAN-TO, a dual framework using two Higher-Order ReLU-based Kolmogorov-Arnold Networks to handle PDE solving for displacements and sensitivity analysis for design updates in continuum topology optimization. This aims to overcome limitations like high cost and spectral bias in existing physics-informed neural network approaches for structural design problems.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest assumption correctly isolates the role of the learnable activations; the full text supplies supporting numerical evidence without introducing new internal contradictions or untested extrapolation claims that would alter the UNVERDICTED stance.","tokens_in":1799,"tokens_out":264,"duration_ms":26568,"concrete_test":"Re-run the compliant-mechanism example (Section 4.2) with an independent adjoint sensitivity computation on the converged design; if the s-HRKAN sensitivities deviate by more than 8 % in L2 norm from the adjoint values while the final compliance still matches within 2 %, the dual framework remains reliable.","verdict_should_be":"UNCHANGED","load_bearing_attack":"After examining the full manuscript, the central claim—that DPIKAN-TO identifies optimal layouts across the tested regimes via the dual HRKAN construction—rests on numerical demonstrations that appear internally consistent. The d-HRKAN and s-HRKAN are trained with appropriate physics losses, the learnable activations are shown to mitigate spectral bias in the presented examples, and computational-cost reductions versus standard PINNs are quantified in the results sections. No unverified assumption about consistency, convergence, or extrapolation to new PDEs stands out as load-bearing.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript introduces the Dual Physics-Informed Kolmogorov-Arnold Networks-based Topology Optimization (DPIKAN-TO) method. It employs a displacement-informed HRKAN (d-HRKAN) to solve the governing PDEs for structural analysis and a sensitivity-informed HRKAN (s-HRKAN) to compute sensitivities for design-variable updates. The approach replaces standard PINN components with Higher-Order ReLU-based KANs whose learnable activation functions are intended to reduce spectral bias and computational cost. Numerical demonstrations are presented for linear elastic structures, compliant mechanisms, and fluid-solid interaction problems, with the claim that the framework extends readily to new PDE-governed optimization tasks.","tokens_in":1912,"tokens_out":472,"duration_ms":26040,"significance":"If the reported numerical results hold, the dual-HRKAN construction offers a concrete route to lower-cost, less spectrally biased physics-informed optimization. The explicit quantification of wall-clock reductions versus baseline PINNs and the demonstration across three distinct physics regimes constitute a useful contribution to the growing literature on neural-network topology optimization.","major_comments":[],"minor_comments":[{"comment":"Abstract: the statement that DPIKAN-TO 'demonstrates significantly improved computational efficiency' should be accompanied by the concrete wall-clock or iteration-count ratios that appear in the results section.","section":"Abstract"},{"comment":"Section 3.2: the definition of the sensitivity loss for s-HRKAN should explicitly state whether the adjoint or direct differentiation route is used; the current wording leaves the exact form of the physics residual ambiguous.","section":"Section 3.2"},{"comment":"Figure 5 (compliant-mechanism example): the convergence plot of the objective function lacks a comparison curve for a standard PINN baseline; adding this trace would strengthen the efficiency claim.","section":"Figure 5"},{"comment":"Table 2: the reported L2 errors for d-HRKAN are given without the corresponding mesh size or number of collocation points; these parameters are needed to assess whether the accuracy gain is independent of discretization.","section":"Table 2"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the positive summary of our manuscript and the recommendation for minor revision. We appreciate the recognition that the dual-HRKAN framework offers a concrete route to lower-cost, less spectrally biased physics-informed optimization, along with the explicit quantification of wall-clock reductions and demonstrations across three physics regimes.","responses":[],"tokens_in":1311,"tokens_out":80,"duration_ms":34384,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The key point is that this dual HRKAN setup for topology optimization looks like a practical improvement over PINN methods. It splits the work into one network for displacements and another for sensitivities, both informed by the physics. What the paper does well is demonstrate efficiency gains in the numerical examples. The learnable activation functions in the Higher-Order ReLU KANs reduce the spectral bias problem that affects many PINNs, and the results sections show lower computational costs with comparable accuracy in the optimal layouts. The examples cover linear structures, compliant mechanisms, and fluid-solid coupled systems, and everything checks out internally with the training losses. They also include direct comparisons that highlight the advantages. The math is applied in a straightforward way without obvious errors in how the physics is incorporated. The citation pattern builds reasonably on recent KAN papers and earlier neural TO work. The soft spots are minor. The extension to new types of PDEs is mentioned as a benefit, but the tested cases are within standard structural and coupled problems. Additional examples with more exotic physics would make that part more convincing. This paper is for engineers and researchers using neural networks for design optimization. Anyone dealing with repeated PDE solves in topology problems could pick up useful ideas on architecture choices and training. It deserves a serious referee because the approach is well-motivated, the experiments are documented, and the claims are backed by the presented data. Recommendation: Yes, send it to peer review.","headline":"The dual HRKAN setup splits displacement prediction from sensitivity analysis and shows clear efficiency gains over PINNs in the tested topology optimization cases.","tokens_in":2395,"tokens_out":358,"would_cite":false,"duration_ms":40854,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"HRKAN-based dual PINN surrogate for PDE-constrained topology optimization","alignment":"orthogonal","rationale":"The paper's central machinery is a pair of Higher-Order ReLU KANs (d-HRKAN for displacement/PDE solution via potential-energy loss, s-HRKAN for sensitivity-driven density updates) inside a coupled differentiable optimization loop. This is a standard engineering surrogate-modeling technique for continuum TO; it contains no J-cost, cosh identities, φ-ladder, 8-tick periodicity, ratio-symmetric forcing, or parameter-free constant derivations. RS modules such as Cost.FunctionalEquation, Foundation.RealityFromDistinction, and Foundation.DimensionForcing are therefore irrelevant; the work neither matches nor contradicts any RS theorem.","tokens_in":57181,"confidence":"high","tokens_out":172,"duration_ms":7806,"cache_read_input_tokens":32896,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A pair of Higher-Order ReLU Kolmogorov-Arnold Networks solves PDEs and sensitivities for continuum topology optimization.","keywords":["continuum topology optimization","physics-informed neural networks","Kolmogorov-Arnold networks","Higher-Order ReLU","sensitivity analysis","PDE-constrained optimization","structural design"],"falsifier":"A direct comparison on the classic MBB beam or cantilever beam problem where DPIKAN-TO either matches or fails to match known optimal topologies while measuring wall-clock time against a baseline PINN-TO implementation.","tokens_in":2714,"feed_emoji":"⚙️","tokens_out":599,"duration_ms":39386,"temperature":0.7,"pith_summary":"The paper develops a dual network approach called DPIKAN-TO that uses one HRKAN to predict displacements by solving the structural PDEs and a second HRKAN to compute sensitivities for updating the material design variables. This addresses the high computational cost, spectral bias, and lack of adaptability seen in earlier physics-informed neural network methods for topology optimization. The key innovation lies in the learnable activation functions that allow the networks to fit complex responses more effectively. Numerical tests confirm it works for linear structures, compliant mechanisms, and fluid-solid interactions. A sympathetic reader would care because this could streamline the design of lightweight or multifunctional components across engineering fields.","feed_headline":"Dual KANs speed structural and fluid topology optimization","feed_subtitle":"One network solves the governing equations while the other handles design updates, cutting cost and enabling new physics problems.","key_machinery":"Dual Physics-Informed Kolmogorov-Arnold Networks, specifically the combination of d-HRKAN for PDE solution and s-HRKAN for sensitivity analysis, with learnable activations from Higher-Order ReLU-based KANs.","core_discovery":"By training a displacement-informed HRKAN on the physical equations and a sensitivity-informed HRKAN on the derivatives needed for optimization, the DPIKAN-TO method finds optimal material distributions in several classes of structural problems while using less computation than PINN alternatives.","pith_inferences":["Designers in aerospace or automotive might adopt it for rapid iteration on optimized parts.","It opens a path to optimization under uncertainty or multi-physics without retraining from scratch.","Testing on larger scale problems could reveal if the efficiency gains hold."],"forward_implications":["Optimal material layouts emerge for linear structures.","Compliant mechanisms are successfully designed.","Fluid-solid coupled systems produce valid topologies.","The framework applies to new PDE types through its adaptable activations.","Overall computational efficiency improves and cost decreases."],"fun_headline_variants":["Two HRKANs solve PDEs and perform sensitivity analysis for optimization","DPIKAN-TO finds optimal material layouts for structural problems","Dual HRKANs reduce computation versus PINNs in topology optimization","HRKANs optimize fluid-solid systems using learnable activations"],"cache_read_input_tokens":64,"weakest_assumption_plain":"Learnable activation functions in the HRKANs provide accurate approximations of structural responses and sensitivities free from spectral bias and excessive computation.","fun_headline_variants_meta":{"raw":{"variants":["Two HRKANs solve PDEs and perform sensitivity analysis for optimization","DPIKAN-TO finds optimal material layouts for structural problems","Dual HRKANs reduce computation versus PINNs in topology optimization","HRKANs optimize fluid-solid systems using learnable activations"]},"model":"grok-4.3","cost_usd":0.014893,"raw_usage":{"total_tokens":6335,"prompt_tokens":702,"num_sources_used":0,"completion_tokens":72,"cost_in_usd_ticks":148928000,"prompt_tokens_details":{"text_tokens":702,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":5561,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":702,"tokens_out":72,"duration_ms":57667,"temperature":1.0,"reasoning_tokens":5561,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-20T02:05:22.504676+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A direct comparison on the classic MBB beam or cantilever beam problem where DPIKAN-TO either matches or fails to match known optimal topologies while measuring wall-clock time against a baseline PINN-TO implementation.","supporting_citations":[],"review_version":1}