{"id":"c013209d-00eb-407e-9607-866ce7a726f6","arxiv_id":"2607.15492","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A differentiable solver for cardiac reaction-diffusion waves recovers hidden states and parameters of the Aliev-Panfilov model from sparse, surface-only, or noisy voltage observations, including two experimental monolayer spirals.","lead":"This paper shows that simulations of electrical waves in heart tissue can be fitted automatically to video or sparse electrode data by backpropagating through the solver, recovering unobserved wave states and model parameters. If it generalizes to clinical recordings, it could help locate arrhythmia sources and build patient-specific heart models.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Voltage-only identifiability is assumed, not established; Section III C shows a degenerate intramural solution, so the broad recovery claim may not generalize beyond chaotic reentrant dynamics.","rationale":"The reader's weakest assumption identifies the same load-bearing concern: the inverse problem of recovering hidden state and parameters from voltage-only observations is assumed identifiable without proof. Section III C provides an explicit counterexample within the paper, showing that small epicardial loss does not imply correct intramural recovery. This is the most fundamental condition for the central claim, and it remains unresolved. My proposed test—a singular-value analysis of the sensitivity matrix or a stationary-spiral recovery experiment—would empirically characterize when the map is identifiable and would either support or refute the generality of the method. Since the reader already issued a CONDITIONAL verdict with this concern central, my finding does not change the verdict.","tokens_in":31046,"tokens_out":6017,"duration_ms":71488,"concrete_test":"For a representative spiral-wave trajectory (parameters of Fig. 5) and a focal-wave trajectory (Fig. 4), compute the sensitivity matrix J = d(v_obs)/d(v0, r0, theta) over the observation window using automatic differentiation, and report its singular values. If the focal-wave J has condition number > 1e4 or multiple near-zero singular values while the spiral-wave J is well-conditioned, the identifiability concern is confirmed. Alternatively, run the optimization with 10 random initial guesses on a stationary (non-meandering) spiral wave; if parameter recovery fails or converges to different values, the dependence on 'rich dynamics' is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that observing only v on a subset of space-time uniquely determines the hidden state (v0, r0) and parameters theta. This identifiability premise is introduced in Section II C and never analyzed. The paper itself demonstrates the failure mode in Section III C: after single-horizon fitting to epicardial observations, the epicardial loss is negligible yet the intramural pattern 'might be a degenerate solution' and the septal focus is distorted. This shows the observation-to-state map is not injective in general. The successful spiral/scroll cases (Sections III B, III D) recover parameters to <0.05–0.3% and co-evolve for tens of rotations, but those dynamics are chaotic or meandering and likely more informative. The authors state in Section IV that learning is less effective for focal or stationary waves. Therefore the broad statement in the abstract—'recover the full dynamics, even with sparse, noisy, or partial observations'—is not supported; the conditions under which the inverse problem is identifiable are uncharacterized.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a fully differentiable cardiac electrophysiology simulation framework, implemented in JAX for finite-difference (2D/3D regular grids) and smoothed-particle-hydrodynamics (SPH) for heart-shaped geometries, and uses gradient-based optimization to estimate model parameters and the dynamical state from spatio-temporal voltage observations. The central method is a rolling multi-horizon learning schedule that sequentially fits overlapping time windows, which the authors show is critical for avoiding saturation and achieving parameter convergence. The claims are supported by in-silico experiments: recovery of all six Aliev-Panfilov parameters to <0.05–0.3% error for 2D spiral and 3D scroll waves, with out-of-sample co-evolution for tens of rotations; recovery of 2D multi-spiral dynamics from sparse electrode-grid observations; localization of intramural focal sources in a biventricular geometry from epicardial observations; and a cross-model fit of the AP model to Mitchell-Schaeffer data. For experimental monolayer imaging data, the authors augment the pixel-wise loss with a V-JEPA perceptual loss and use a diffusion model for initialization/constraint, showing fits to calcium and voltage spirals that remain visually congruent for several rotations. The paper is a proof-of-principle rather than a clinical tool, and it emphasizes that the method is most effective for complex chaotic reentrant dynamics.","tokens_in":31315,"tokens_out":3918,"duration_ms":48853,"significance":"If the quantitative recovery results hold, this is a substantial advance for state and parameter estimation in cardiac electrophysiology. The strongest evidence is the out-of-sample co-evolution test: after learning from about 4 spiral rotations, the fitted simulation and ground truth remain congruent for 20–30 rotation periods, and similar long-horizon agreement is demonstrated for 3D scroll waves from surface-only observations. The paper also introduces useful practical ingredients: the rolling multi-horizon schedule, a V-JEPA perceptual loss for noisy experimental data, and a DDPM-based initialization that projects initial states onto the model manifold. The SPH implementation on a realistic ventricular geometry extends differentiable-physics fitting beyond regular grids. The main weakness is that the identifiability premise—recovering hidden state and parameters from voltage-only, possibly partial observations—is asserted but not analyzed, and the paper itself documents a degeneracy in the biventricular focal case. This limits the transferability of the quantitative success to the experimental and clinical regimes.","major_comments":[{"comment":"The paper's central premise is that observing only the voltage variable v on a subset of space-time determines the hidden state (v0, r0) and all parameters θ. This identifiability assumption is introduced in Section II C and never analyzed. The paper itself provides a counterexample in Section III C: after single-horizon fitting to epicardial observations, the epicardial loss is negligible while the intramural pattern 'might be a degenerate solution' and the septal focus is distorted. The abstract's broad claim—'recover the full dynamics, even with sparse, noisy, or partial observations'—is therefore not supported. The authors should either characterize the conditions under which the inverse problem is identifiable (e.g., via observability analysis or a parameter-sensitivity study) or restrict the claim to chaotic reentrant dynamics, which are empirically more informative.","section":"Section II C and III C"},{"comment":"In the rolling multi-horizon schedule, each new horizon re-initializes the state using the second learned state of the previous horizon and the observed voltage at the new horizon boundary (Eq. 11 and surrounding text). This periodically re-anchors the simulation to ground-truth observations during training, so the parameter gradients are accumulated across teacher-forced windows rather than a single free-running trajectory. The out-of-sample forecast is a valid control, but the paper does not report an ablation in which the learned parameters/state are evaluated without such re-anchoring during training. This makes it difficult to attribute the parameter recovery accuracy to the differentiable solver alone versus the re-anchoring schedule. A control experiment (e.g., fitting with only the first horizon and then forecasting) would clarify the mechanism.","section":"Section II C 3 and III B"},{"comment":"The experimental fits are evaluated qualitatively: the text states that the simulated spiral is 'slightly slower' or 'slightly faster' and that the two co-evolve for 'about 4–5 rotations' before divergence, but no quantitative error metric, action-potential-duration comparison, conduction-velocity comparison, or phase-singularity-trajectory error is provided. Given the paper's claim that the method transfers to real experimental footage, a quantitative assessment of the fit quality (even a simple pixel-wise or phase-based error over the co-evolution window) is needed. Without it, the experimental section remains a visual demonstration rather than a measured validation.","section":"Section III G, Fig. 17"},{"comment":"The paper reports that parameter errors for focal waves are 1–5% for {ε0, μ1, μ2} (Table IV) and states in Section IV that learning is less effective for focal or stationary waves. This is a limitation of the method for an important class of cardiac rhythms (pacing, premature beats). The authors should state this limitation prominently in the abstract or introduction, since the current abstract implies universal applicability. The technical explanation offered—that complex dynamics are more informative—is plausible but not tested; a brief analysis or a more cautious wording would improve the paper.","section":"Section III A and IV"}],"minor_comments":[{"comment":"The regularization loss uses the symbol u in max(-u,0) but the state variables are v and r; presumably u is a typo for v. Please clarify.","section":"Eq. (6)"},{"comment":"The caption text is corrupted: 'With 27 horizons, the dynamics are identical over 20 rotations. or 67 time steps or 20,000 epochs, the dynamics is learned overCTop row:' contains a truncated sentence. Please rewrite the caption.","section":"Fig. 5B"},{"comment":"The perceptual loss Lp is written as a sum over t of a quotient. The notation for the ℓ2-normalized features is ambiguous; please define N or use explicit vector norms for each frame, e.g., ||fθ(v't)||2.","section":"Section II C 1, Eq. (9)"},{"comment":"The phrase 'with strides=1' appears to be a typo; the intended term is 'stride'. Also, the construction (v',r')_{i-1,2} → (v_bar,r')_{i,1} is not fully explained in the main text; consider a diagram or a more explicit definition.","section":"Section II C 3"},{"comment":"The description of the DDPM initialization states that the model can translate MS voltage patterns into AP spirals with both components, but the SDEdit/RePaint procedure is only outlined. Since this is a key component for the experimental fits, a more detailed description in the supplement would be helpful.","section":"Section II C 4"},{"comment":"The source code is stated to be available upon publication, but no repository link is provided in the manuscript. Please add a data/code availability statement with a URL.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper is a strong proof-of-principle for differentiable cardiac EP simulation, and the out-of-sample co-evolution results are impressive. The main concern is that the breadth of the claims (full dynamics from partial observations) exceeds what is demonstrated; the identifiability issue is acknowledged in Section III C but not resolved. I would recommend major revision: the authors should either provide an observability analysis or significantly temper the abstract and introduction. The multi-horizon re-anchoring ablation and quantitative experimental evaluation should also be addressed. The methodology itself is sound and the contributions are significant, so this is not a reject."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a serious methods paper. The core idea - multi-horizon differentiable fitting of cardiac EP models to voltage observations - is not entirely new, but the combination of overlapping horizons, state re-anchoring, and the range of test settings is a real step forward. The in-silico results are the strongest part: spiral-wave parameters recovered to under 0.05%, 3D scroll waves from surface observations to under 0.3%, and the learned simulations co-evolve with ground truth for 20-40 rotations after training. That is a genuine predictive test, not just a fit to the training window. The comparison with prior work is fair: Lettermann et al. needed the full initial state, and Kashtanova et al. used hybrid neural corrections. The sparse-grid, cross-model, and experimental demonstrations are appropriate proof-of-concept.\n\nThe main soft spot is the identifiability problem. The paper assumes that observing only voltage on a subset of space-time determines the hidden refractory field and the parameters, but this is never analyzed. The paper itself shows the failure mode in Section III C: after single-horizon fitting to epicardial observations, the epicardial loss is tiny while the intramural pattern is degenerate. The authors acknowledge this and even say in the Discussion that the method is less effective for focal or stationary waves. That sits uneasily with the abstract's claim to recover the full dynamics, even with sparse, noisy, or partial observations. The paper should either narrow the claims or provide some analysis of when the inverse problem is identifiable. This is the load-bearing issue for the translational claims.\n\nOther soft spots are more minor. The experimental fits are qualitative - no error metrics, and the V-JEPA/DDPM components are described as necessary but not ablated or robustly tested. The multi-horizon schedule is heavily tuned; the paper shows it matters, but not how sensitive the method is to those hyperparameters. The code is promised upon publication, which is fine for a preprint but needs to be delivered.\n\nNone of this is fatal. The central demonstration holds for chaotic spiral and scroll waves, which are the clinically interesting arrhythmia regimes. The paper deserves a serious referee, and I would not desk reject it. The referee should push on identifiability, ask for quantitative experimental evaluation, and request a robustness analysis of the scheduling and loss components.","headline":"Serious methods paper with strong in-silico evidence for chaotic reentrant dynamics, but the abstract overclaims and the voltage-only identifiability question is never addressed.","tokens_in":734,"tokens_out":1002,"would_cite":true,"duration_ms":35420,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["92C30","35K57","65M06","65M75"],"pacs":[],"model":"deepseek-v4-flash","headline":"A fully differentiable heart-wave simulator recovers hidden states and parameters from voltage-only observations, forecasting chaotic spiral dynamics 20-30 rotations ahead after learning only 4-5 rotations.","keywords":["differentiable simulations","cardiac electrophysiology","state estimation","parameter estimation","spiral waves","scroll waves","reaction-diffusion","digital twin"],"falsifier":"A concrete check: construct two different (parameter, initial-state) configurations that produce identical voltage observations at all observed points and times (or differing below noise level) while having materially different hidden refractory fields; if such colliding configurations exist, the recovery is provably non-unique. A simpler experiment is to run the biventricular focal fitting with several random initializations and check whether the septal focus location and intramural pattern remain stable or vary across runs, as the paper already reports one distorted septal focus.","tokens_in":30870,"feed_emoji":"🫀","tokens_out":4775,"duration_ms":56715,"temperature":0.7,"pith_summary":"The paper shows that making cardiac electrophysiology simulations fully differentiable lets gradients from a simple voltage-mismatch loss flow back through the PDE solver, jointly recovering unknown model parameters and the complete initial dynamical state, including the hidden refractory variable. With a rolling schedule of short, overlapping training windows, the learned simulation co-evolves with the ground truth for tens of spiral rotations even though the dynamics are chaotic. The same machinery handles sparse electrode-grid data, surface-only observations of 3D scroll waves, and experimental optical-mapping recordings when augmented with a perceptual loss and a diffusion-model-based initialization. If correct, this offers a concrete route to personalizing heart models from the partial, noisy measurements available in clinical and experimental settings.","feed_headline":"Simulator trained on 4 rotations forecasts 20 rotations of heart waves","feed_subtitle":"Gradient descent through the solver recovers hidden cardiac state from voltage snapshots alone.","key_machinery":"The load-bearing mechanism is an end-to-end differentiable PDE solver: the entire finite-difference or smoothed-particle-hydrodynamics integration is written in a way that permits exact reverse-mode gradients of the observation loss with respect to both the model parameters and the initial state. Around this, the decisive component is the rolling multi-horizon schedule - many short (10-40 time-step) overlapping horizons shifted by one time step - which prevents loss saturation and progressively refines the state and parameters; single long horizons plateau. A smoothness penalty on the hidden refractory field enables sparse-electrode recovery, and for experimental data a perceptual loss compu","core_discovery":"The central claim is that gradient descent through a differentiable reaction-diffusion solver can solve the joint state-and-parameter estimation problem for cardiac tissue: observing only the voltage variable v on part of the domain over time, the method recovers the six parameters of a two-variable phenomenological model and the full initial (v0,r0) fields, with parameter errors under 0.05% for 2D spirals, 0.003-0.3% for 3D scroll waves, and 1-11% for focal or sparse-data cases. The strongest demonstration is long-horizon forecasting: after learning about 4-5 rotations of spiral-wave dynamics, the fitted simulation and the ground-truth system remain congruent for 20-30 rotations into the fu","pith_inferences":["The success on chaotic spirals suggests the method leverages the system's sensitive dependence: the chaotic attractor's dense sampling provides rich gradient information, implying the method is strongest precisely for the complex arrhythmic regimes where clinical prediction is hardest, and weakest for simple focal waves - consistent with the paper's own error trends.","If identifiability holds, the recovered refractory field constitutes a full tomographic reconstruction of transmural electrical state from surface data; a direct test would be to withhold some intramural electrode recordings from the fit and predict them.","The observed degeneration of intramural foci in the biventricular case indicates that observation time, not just spatial resolution, is a fundamental resource; translating to patients may require longer recordings or multiple episodes to disambiguate the hidden state.","A natural extension is to probe models with more state variables (e.g., ionic models); the method's identifiability with respect to hidden variables would likely degrade as model dimension grows, suggesting a trade-off between biophysical detail and recoverability."],"forward_implications":["If the central claim holds, clinically relevant hidden quantities become estimable: intramural early-activation sites and transmural reentrant wave patterns can be reconstructed from epicardial or dual-surface optical mapping.","Sparse multi-electrode-array recordings would suffice to reconstruct full-resolution reentrant dynamics, going beyond activation-time maps to the complete voltage and refractory fields.","Since chaotic spiral dynamics are forecast 20-30 rotations after only 4-5 rotations of observation, the approach could support prediction of arrhythmia evolution rather than mere diagnosis.","The multi-horizon schedule is a general recipe: it enables convergence even when initial parameter guesses are off by 50-100%, whereas single-horizon fitting saturates.","Model-to-model fitting suggests the framework can test how well candidate biophysical models reproduce observed dynamics, and the experimental fits point to a practical pipeline for real imaging data."],"fun_headline_variants":["4 rotations of data forecast 20 rotations of heart waves","Gradient descent through cardiac PDE solver recovers state and parameters","From sparse voltage data, learn heart dynamics and forecast ahead","Differentiable cardiac simulations fit to sparse data, forecast long-term"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire recovery rests on the assumption that observing only the voltage variable over time uniquely determines the hidden refractory state, the initial condition, and the six model parameters - an identifiability condition the paper uses but never proves, and whose failure it exhibits locally in the biventricular focal case, where the recovered intramural pattern is called a degenerate solution.","fun_headline_variants_meta":{"raw":{"variants":["4 rotations of data forecast 20 rotations of heart waves","Gradient descent through cardiac PDE solver recovers state and parameters","From sparse voltage data, learn heart dynamics and forecast ahead","Differentiable cardiac simulations fit to sparse data, forecast long-term"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000785,"raw_usage":{"total_tokens":3348,"prompt_tokens":835,"completion_tokens":2513,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":579,"completion_tokens_details":{"reasoning_tokens":2444}},"tokens_in":579,"tokens_out":2513,"duration_ms":19606,"temperature":1.0,"reasoning_tokens":2444,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T23:11:03.983176+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete check: construct two different (parameter, initial-state) configurations that produce identical voltage observations at all observed points and times (or differing below noise level) while having materially different hidden refractory fields; if such colliding configurations exist, the recovery is provably non-unique. A simpler experiment is to run the biventricular focal fitting with several random initializations and check whether the septal focus location and intramural pattern remain stable or vary across runs, as the paper already reports one distorted septal focus.","supporting_citations":[],"review_version":1}