{"id":"983ff714-e15a-4a11-9e3f-3fc68e300379","arxiv_id":"2606.25323","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"PINN approach for time-domain Maxwell equations with split-field PMLs uses uniform equations across domains and matches analytical/FDTD results on 1D/2D Gaussian pulse tests.","lead":"This paper develops a physics-informed neural network formulation for solving time-domain Maxwell equations that incorporates split-field perfectly matched layers, allowing the same governing equations to apply in both physical and absorbing regions. A smart generalist might read it to see how neural networks could simplify open-boundary electromagnetic simulations compared to traditional finite-difference methods.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption correctly flags a practical risk for any PINN, but the paper's modest claim (feasibility on elementary test problems) does not require that risk to be absent; the evidence presented is consistent with the limited scope asserted.","tokens_in":1656,"tokens_out":255,"duration_ms":10630,"concrete_test":"Reproduce the 1-D Gaussian-pulse experiment using the exact network architecture, collocation-point density, and optimizer schedule reported in the manuscript; confirm that the L2 error against the analytical solution remains below the threshold shown in the paper's figure.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is a feasibility demonstration: a split-field PML formulation allows the same governing equations (and thus the same loss terms) to be used inside and outside the PML region, and standard PINN training produces solutions that visually match analytical/FDTD references on 1D and 2D Gaussian-pulse test cases. Because the claim is limited to these simple, short-time, low-dimensional problems and does not assert generality, robustness, or superiority over FDTD, no internal inconsistency or unsupported step is visible from the given information.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper presents a PINN formulation for the time-domain Maxwell equations that incorporates split-field PMLs. A stated advantage is that the same governing equations apply in both the physical and PML regions, simplifying loss construction. The method is validated on 1D and 2D Gaussian pulse problems, with the claim that PINN solutions show good agreement with analytical and FDTD references, demonstrating feasibility for open-domain time-domain EM simulations.","tokens_in":1753,"tokens_out":355,"duration_ms":16665,"significance":"If the implementation details and quantitative support are supplied, the work would establish the feasibility of a uniform-equation PINN approach for Maxwell problems with split-field PMLs on simple low-dimensional test cases. This could reduce the complexity of loss-term construction relative to other PML formulations, though the demonstration is restricted to short-time Gaussian pulses without claims of generality or superiority over FDTD.","major_comments":[{"comment":"Abstract and validation sections: the claim of 'good agreement' is asserted without any reported network architecture (layers, width, activations), loss-term weights, optimizer hyperparameters, training schedule, or convergence diagnostics. These elements are required to evaluate whether the optimizer reliably solves the coupled system that includes the split-field auxiliary equations.","section":"Abstract and numerical results"},{"comment":"Validation sections: support for the central feasibility claim rests solely on visual field plots; no quantitative error measures (relative L2 norms, pointwise maxima, or integrated residuals) or comparison tables against the FDTD reference are supplied, preventing assessment of accuracy beyond qualitative inspection.","section":"Numerical experiments"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed and constructive report. The two major comments correctly identify gaps in the presentation of implementation details and quantitative validation. We will revise the manuscript to address both points fully.","responses":[{"response":"We agree that these implementation details are essential for reproducibility and for assessing whether the optimizer successfully handles the coupled split-field system. In the revised manuscript we will add a new subsection (or appendix) that reports the network architecture (depth, width, activation functions), the relative weights assigned to each term in the composite loss, the optimizer and its hyperparameters, the training schedule (including any adaptive weighting or curriculum strategies), and convergence diagnostics such as loss histories and residual norms. These additions will directly address the concern about reliable solution of the auxiliary equations.","revision_made":"yes","referee_comment":"[Abstract and numerical results] Abstract and validation sections: the claim of 'good agreement' is asserted without any reported network architecture (layers, width, activations), loss-term weights, optimizer hyperparameters, training schedule, or convergence diagnostics. These elements are required to evaluate whether the optimizer reliably solves the coupled system that includes the split-field auxiliary equations."},{"response":"We accept that visual agreement alone is insufficient for a rigorous feasibility demonstration. The revised manuscript will include quantitative error metrics: relative L2 norms of the electric and magnetic field components over the computational domain at selected time instants, maximum pointwise errors, and integrated residual norms of the governing equations. We will also add a table that directly compares these quantities against the FDTD reference solutions for both the 1-D and 2-D test cases. This will allow readers to evaluate accuracy beyond qualitative inspection.","revision_made":"yes","referee_comment":"[Numerical experiments] Validation sections: support for the central feasibility claim rests solely on visual field plots; no quantitative error measures (relative L2 norms, pointwise maxima, or integrated residuals) or comparison tables against the FDTD reference are supplied, preventing assessment of accuracy beyond qualitative inspection."}],"tokens_in":1291,"tokens_out":438,"duration_ms":11900,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The central point is that this paper takes the split-field PML formulation for time-domain Maxwell equations and puts it into a PINN loss. Because the split-field version keeps the same governing equations inside and outside the PML region, the loss construction stays uniform and does not need extra terms or switches.\n\nThey test the idea on one- and two-dimensional Gaussian pulse problems and report that the PINN solutions line up with analytical and FDTD references. That part is straightforward and shows the basic compatibility.\n\nThe work is honest about its scope: it is a feasibility check on short-time, low-dimensional cases rather than a claim of broad superiority or robustness. The simplification from using split-field PMLs is real and worth noting for anyone already building PINN losses for wave problems.\n\nThe main limitation is the lack of concrete numbers. The abstract gives no architecture details, no loss weights, no training hyperparameters, and no quantitative error metrics or convergence plots. Without those, it is hard to judge how reliably the optimizer handles the extra auxiliary variables or whether the agreement holds beyond the visual level on these simple pulses.\n\nThis is for readers who already work on PINNs for electromagnetics and want to see an open-boundary example. It will not interest people looking for new theory or large-scale engineering results.\n\nIf the full paper supplies the missing implementation details, error tables, and perhaps code, it deserves peer review. The idea itself is clean and the tests are appropriate for the claim being made.","headline":"Split-field PMLs let the same Maxwell equations go into the PINN loss everywhere, and the method matches references on basic 1D/2D pulses, but the support is only visual and the tests stay elementary.","tokens_in":2245,"tokens_out":392,"would_cite":false,"duration_ms":15821,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Physics-informed neural networks solve time-domain Maxwell equations in open domains by incorporating split-field PMLs into the loss.","keywords":["physics-informed neural networks","Maxwell equations","split-field PML","time-domain electromagnetics","open-domain simulations","Gaussian pulse propagation"],"falsifier":"A significant deviation between the PINN solution and the FDTD reference on the reported one- or two-dimensional Gaussian pulse problems, especially in the PML region where waves should decay without reflection, would show the formulation fails to deliver accurate results.","tokens_in":2561,"feed_emoji":"⚡","tokens_out":349,"duration_ms":16401,"temperature":0.7,"pith_summary":"The paper establishes a PINN formulation for the time-domain Maxwell equations that incorporates split-field perfectly matched layers. This approach uses the same governing equations in both the physical domain and the PML regions, which simplifies loss construction. Validation on one-dimensional and two-dimensional Gaussian pulse problems shows that the resulting solutions agree with analytical and FDTD reference solutions.","feed_headline":"Split-field PMLs let PINNs solve open Maxwell problems uniformly","feed_subtitle":"Same equations govern physical and absorbing regions, matching FDTD references on 1D and 2D pulse tests.","key_machinery":"The split-field perfectly matched layer formulation, which absorbs outgoing waves while preserving identical Maxwell equations in physical and PML regions.","core_discovery":"By embedding the auxiliary equations of the split-field PML directly into the PINN loss function, the same set of equations governs wave propagation throughout the entire domain, enabling accurate open-domain solutions without separate boundary treatments or region-specific modifications.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Split-field PML unifies PINN equations for Maxwell","PINN applies same Maxwell equations in PML and physical areas","Embedded split PML in PINN loss for open domain solutions","Split PML simplifies PINN to uniform Maxwell formulation","PINNs handle Maxwell with split-field PML without region splits"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"A standard neural-network optimizer can reliably converge to an accurate solution of the coupled PDE system when the split-field PML auxiliary equations are included in the loss without additional stabilization or weighting adjustments.","fun_headline_variants_meta":{"raw":{"variants":["Split-field PML unifies PINN equations for Maxwell","PINN applies same Maxwell equations in PML and physical areas","Embedded split PML in PINN loss for open domain solutions","Split PML simplifies PINN to uniform Maxwell formulation","PINNs handle Maxwell with split-field PML without region splits"]},"model":"grok-4.3","cost_usd":0.005551,"raw_usage":{"total_tokens":2620,"prompt_tokens":584,"num_sources_used":0,"completion_tokens":76,"cost_in_usd_ticks":55512000,"prompt_tokens_details":{"text_tokens":584,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1960,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":584,"tokens_out":76,"duration_ms":14264,"temperature":1.0,"reasoning_tokens":1960,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-25T20:20:26.912535+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A significant deviation between the PINN solution and the FDTD reference on the reported one- or two-dimensional Gaussian pulse problems, especially in the PML region where waves should decay without reflection, would show the formulation fails to deliver accurate results.","supporting_citations":[],"review_version":1}