{"id":"0597567e-a134-42d6-915d-bf927e2c8512","arxiv_id":"2605.27578","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Transformer encoder plus anisotropic RBF decoder predicts coronary pressure and WSS from centerlines, cutting mean relative L2 error 52% vs best baseline on multi-vessel data at 13.8x lower FLOPs than GNOT.","lead":"The paper introduces a neural framework that encodes 1D coronary artery centerlines plus inlet flow with a transformer and decodes continuous pressure and wall shear stress fields using an anisotropic RBF decoder aligned to vessel shape. It reports lower errors than neural-operator baselines on two new simulation datasets while using far less compute than CFD.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Synthetic training distribution (random stenoses + steady-state OpenFOAM) may not match real-patient coronary variability","rationale":"The reader’s weakest_assumption correctly isolates the single condition required for the applied claim to hold. The internal comparison on the synthetic test sets is not internally inconsistent, but the motivation (“fast, non-invasive coronary hemodynamics prediction” for CAD assessment) makes the data-distribution gap load-bearing. No other technical flaw in the reported numbers is visible from the supplied text.","tokens_in":1855,"tokens_out":369,"duration_ms":25758,"concrete_test":"Acquire 20–30 real-patient coronary centerlines with matched 4D-flow MRI or high-fidelity pulsatile CFD; run the trained model (both 128- and 1024-center variants) and compute mean relative L2 error on pressure and WSS; if the error rises by >30% relative to the paper’s multi-vessel test set, the distribution mismatch is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline performance numbers (52% relative L2 reduction at 1024 centers, 13.8× FLOPs reduction at 128 centers) are measured exclusively on the two generated datasets. The multi-vessel set starts from ImageCAS centerlines, then applies random stenosis insertion and physiologically plausible but non-patient-specific flow rates, followed by steady-state CFD. Real coronary hemodynamics involve patient-specific lesion distributions, plaque morphology, pulsatile inflow, outlet resistance networks, and wall compliance that are not reproduced by this generation process. If the learned centerline-to-wall mapping exploits statistical artifacts of the random-stenosis procedure rather than the underlying physics, the reported error reductions will not transfer, undermining the claim that the framework supplies a practical non-invasive alternative.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript introduces a transformer-based encoder that processes 1D coronary artery centerlines together with inlet flow rates, paired with an anisotropic RBF decoder to predict continuous wall pressure and wall shear stress fields. Two synthetic datasets are generated via steady-state OpenFOAM simulations: a public single-vessel benchmark with controlled variations and a multi-vessel set derived from ImageCAS centerlines with randomly inserted stenoses and varied flow rates. On held-out splits from these datasets the proposed model reports lower mean relative L2 errors than GNOT, Transolver and ONO baselines (52 % reduction at 1 024 centers on the multi-vessel set) while requiring substantially fewer FLOPs at lower center counts (13.8× reduction versus GNOT at 128 centers).","tokens_in":2011,"tokens_out":560,"duration_ms":39118,"significance":"If the reported error reductions on the synthetic data hold, the anisotropic RBF decoder supplies an efficient centerline-to-wall surrogate that could accelerate hemodynamic assessment relative to full CFD. The public release of the single-vessel dataset is a concrete contribution that enables reproducibility and follow-on work.","major_comments":[{"comment":"§4 (Model) and §5.2 (Ablation experiments): the central performance claims rest on the anisotropy of the RBF centers, yet no ablation isolating anisotropic versus isotropic RBFs is presented; without this comparison it is impossible to attribute the 52 % error reduction specifically to the anisotropy mechanism rather than to the overall architecture or center count.","section":"§4 and §5.2"},{"comment":"§3 (Dataset generation) and §6 (Discussion): the multi-vessel dataset is produced by random stenosis insertion on ImageCAS centerlines followed by steady-state OpenFOAM runs with non-patient-specific flow rates; the manuscript provides no external validation against in-vivo measurements or pulsatile patient-specific CFD, which directly bears on the claim that the framework constitutes a practical non-invasive alternative.","section":"§3 and §6"}],"minor_comments":[{"comment":"Abstract and §5.1: the headline 52 % and 13.8× figures are stated without accompanying standard deviations or test-set sizes, reducing interpretability of the quantitative improvements.","section":"Abstract and §5.1"},{"comment":"Figure 3 and Table 1: axis labels and color scales for the predicted versus ground-truth WSS fields are not described in the caption, making visual assessment of local error patterns difficult.","section":"Figure 3 and Table 1"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive feedback. We address the major comments point by point below.","responses":[{"response":"We agree that demonstrating the specific contribution of anisotropy is important. In the revised version, we will include an ablation experiment that replaces the anisotropic RBF decoder with an isotropic one while keeping the encoder, number of centers, and all other hyperparameters identical. This will allow us to quantify the performance difference attributable to anisotropy alone.","revision_made":"yes","referee_comment":"[§4 and §5.2] §4 (Model) and §5.2 (Ablation experiments): the central performance claims rest on the anisotropy of the RBF centers, yet no ablation isolating anisotropic versus isotropic RBFs is presented; without this comparison it is impossible to attribute the 52 % error reduction specifically to the anisotropy mechanism rather than to the overall architecture or center count."},{"response":"We acknowledge the limitation highlighted. Our work is based on synthetic steady-state data to provide a controlled and reproducible benchmark for the proposed method. Providing in-vivo validation or pulsatile simulations would require new datasets and experiments that are outside the scope of the current manuscript. We will revise the Discussion section to more clearly articulate the assumptions, limitations, and intended scope of the synthetic validation, and suggest pathways for future clinical translation.","revision_made":"partial","referee_comment":"[§3 and §6] §3 (Dataset generation) and §6 (Discussion): the multi-vessel dataset is produced by random stenosis insertion on ImageCAS centerlines followed by steady-state OpenFOAM runs with non-patient-specific flow rates; the manuscript provides no external validation against in-vivo measurements or pulsatile patient-specific CFD, which directly bears on the claim that the framework constitutes a practical non-invasive alternative."}],"tokens_in":1526,"tokens_out":396,"duration_ms":46510,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that the authors encode 1D centerlines and inlet flow with a transformer, then decode to continuous pressure and wall-shear fields using morphology-aligned anisotropic RBFs. On their single-vessel and multi-vessel sets this cuts mean relative L2 error by roughly half versus the strongest baseline while using far fewer FLOPs at low center counts.\n\nThe decoder design is the clearest addition. Standard neural operators do not explicitly tie the basis functions to local vessel orientation the way this one does, and that choice appears to drive the reported improvements at both 128 and 1024 centers. Releasing the single-vessel dataset is also useful; others can now test centerline-to-field mappings without regenerating the CFD labels.\n\nThe soft spot is the training distribution. Both datasets come from steady-state OpenFOAM on geometries that start from ImageCAS centerlines and then receive random stenosis insertion plus simplified flow rates. Real coronary hemodynamics include pulsatile inflow, compliant walls, patient-specific plaque morphology, and outlet resistance networks that are absent here. If the model is learning statistical regularities of the random-stenosis procedure rather than the underlying physics, the error reductions will not transfer. The abstract gives no in-vivo numbers or even pulsatile test cases, so the practical claim stays conditional on how representative the generated data turn out to be.\n\nThis is for groups already working on fast surrogates for vascular CFD or on geometry-aware neural operators. A reader who cares about centerline-based modeling will find the decoder and the direct baseline comparisons worth examining. The paper deserves peer review because the method is concrete, the comparisons are reproducible from the released data, and the central limitation is one that referees can evaluate directly.","headline":"The paper gives a transformer-plus-anisotropic-RBF pipeline that beats neural-operator baselines on two generated coronary datasets, but the gains rest entirely on steady-state simulations with random stenoses.","tokens_in":2512,"tokens_out":430,"would_cite":false,"duration_ms":23965,"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":"A transformer encoder paired with an anisotropic RBF decoder predicts coronary pressure and wall shear stress from centerlines and inlet flow more accurately than neural-operator baselines at far lower cost.","keywords":["coronary hemodynamics","radial basis functions","transformer encoder","wall shear stress","pressure prediction","neural operators","centerline encoding","computational fluid dynamics"],"falsifier":"Comparison of the model's predicted pressure and wall shear stress against either invasive patient measurements or independent high-fidelity CFD on real clinical geometries absent from the training sets.","tokens_in":2746,"feed_emoji":"🫀","tokens_out":762,"duration_ms":39768,"temperature":0.7,"pith_summary":"The paper introduces a framework that encodes one-dimensional vessel centerlines together with inlet flow rate via a transformer and then reconstructs continuous wall pressure and shear-stress fields using an anisotropic radial basis function decoder whose centers follow vessel morphology. Two supporting datasets are created: 4,200 synthetic single-vessel cases with controlled variations and 4,800 multi-vessel cases derived from ImageCAS by adding random stenoses and physiologically plausible flows, each paired with steady-state OpenFOAM solutions. On the multi-vessel set the method lowers mean relative L2 error by 52 percent relative to the strongest baseline while requiring 13.8 times fewer FLOPs than GNOT at 128 centers and still outperforming all competitors. The single-vessel dataset is released publicly to allow further work.","feed_headline":"Anisotropic decoder cuts coronary error by 52 percent","feed_subtitle":"Transformer plus morphology-aligned RBFs beat neural baselines on multi-vessel cases while using 13.8 times fewer operations than GNOT.","key_machinery":"Anisotropic Radial Basis Function decoder aligned with vessel morphology, which reconstructs continuous pressure and wall shear stress fields from a modest number of morphology-aware centers.","core_discovery":"The model encodes 1D vessel centerlines together with inlet flow rate using a transformer-based encoder, and predicts continuous wall-based fields via an anisotropic Radial Basis Function (RBF) decoder aligned with vessel morphology; across both introduced datasets the approach achieves lower pressure and WSS errors than GNOT, Transolver, and ONO at a fraction of CFD cost, with the stated 52 percent error reduction and 13.8 times FLOP reduction on the multi-vessel data.","pith_inferences":["If the mapping holds on real angiograms, the framework could supply rapid non-invasive FFR estimates in clinical pipelines.","The morphology-aligned decoder could be tested on pulsatile rather than steady inlet conditions with only minor input changes.","Analogous centerline-to-field prediction might transfer to cerebral or peripheral arteries if the geometric encoding proves domain-agnostic.","Further ablation of center count below 128 could map the accuracy-cost curve for deployment on limited hardware."],"forward_implications":["Hemodynamic fields can be obtained in real time from routine imaging centerlines without repeated CFD runs.","The same encoder-decoder structure works for both single-vessel and multi-vessel coronary trees.","Computational expense drops by more than an order of magnitude relative to GNOT while accuracy improves.","The released single-vessel dataset enables standardized benchmarking of future centerline-to-hemodynamics models.","Steady-state assumptions suffice for the reported accuracy gains on the generated stenosis distributions."],"fun_headline_variants":["Anisotropic RBF decoder reduces coronary error by 52 percent","Morphology aligned RBF lowers pressure and WSS errors","Centerline transformer and RBF decoder achieve lower errors than baselines","52 percent lower error using 128 anisotropic RBF centers","RBF decoder uses 13.8 times fewer FLOPs than GNOT"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"Steady-state OpenFOAM simulations on randomly stenosed synthetic and ImageCAS-derived geometries supply a training distribution representative enough for the learned centerline-to-wall mapping to generalize to real patient coronary hemodynamics.","fun_headline_variants_meta":{"raw":{"variants":["Anisotropic RBF decoder reduces coronary error by 52 percent","Morphology aligned RBF lowers pressure and WSS errors","Centerline transformer and RBF decoder achieve lower errors than baselines","52 percent lower error using 128 anisotropic RBF centers","RBF decoder uses 13.8 times fewer FLOPs than GNOT"]},"model":"grok-4.3","cost_usd":0.005066,"raw_usage":{"total_tokens":2523,"prompt_tokens":778,"num_sources_used":0,"completion_tokens":82,"cost_in_usd_ticks":50662000,"prompt_tokens_details":{"text_tokens":778,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1663,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":778,"tokens_out":82,"duration_ms":20162,"temperature":1.0,"reasoning_tokens":1663,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-29T14:41:00.152843+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Comparison of the model's predicted pressure and wall shear stress against either invasive patient measurements or independent high-fidelity CFD on real clinical geometries absent from the training sets.","supporting_citations":[],"review_version":1}