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REVIEW 4 major objections 5 minor 72 references

Learning to Predict Global Atrial Fibrillation Dynamics from Sparse Measurements

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Pith's one-line read FibMap reconstructs whole-atria AF dynamics from sparse catheter measurements, beating baselines by over 2x in MAE and 11x in phase-singularity detection.

desk verdict FibMap is a credible proof-of-concept for imputation mapping of AF, but the headline numbers are inflated by weak baselines and a normalization protocol that leaks global amplitude information; worth reviewing with revisions. read the letter →

arxiv 2502.09473 v2 pith:ZHJNBLLX submitted 2025-02-13 cs.LG eess.SP

classification cs.LGeess.SP
keywords atrialfibrillationimputationmappinggraphneuralnetworkrecurrentspatiotemporalphasesingularityelectrophysiologicalpersonalisedablation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Atrial fibrillation cannot currently be mapped globally during a routine procedure: standard sequential contact catheters sample small patches of the atrium, and the disorganised rhythm prevents those patches from being stitched together. This paper claims that a graph recurrent neural network, FibMap, can solve that stitching problem by imputing the unmeasured signals from the sparse patches alone. Trained and validated on 51 whole-atria non-contact recordings, FibMap reports a 2.1-fold lower mean absolute error than the best baseline and a true positive rate of 0.89 for detecting phase singularities, the rotor-like organising centres that are candidate ablation targets. Fine-tuning only patient-specific parameters on real multipolar HD Grid recordings from three patients yields imputation maps whose dynamics correlate with independent whole-atria recordings, indicating patient-specific rather than generic reconstructions. If the results hold, routine catheters could produce continuous global maps of AF without expensive non-contact systems, enabling phenotype-guided personalised ablation.

What carries the argument

The engine is a bidirectional gated graph recurrent neural network (GRNN), a non-linear state-space model. The atrium is discretised into a triangulated mesh of 500 nodes, and message passing along mesh edges propagates information from observed patches across space and time; bidirectional processing lets each imputed value draw on both past and future observations. Two learned embedding vectors carry the patient-specific information: a node embedding per mesh node encodes local tissue properties, and a patient embedding encodes global dynamics, while all other parameters are shared across patients to learn common wave-propagation physics. Training uses a self-supervised whole-atria reconstruction loss on randomly sampled catheter paths; for a new patient only the embeddings are fine-tuned with an observed-patch loss, which the authors show correlates with whole-atria loss (Pearson r=0.97). The decoder is trained as a quantile regressor, so each reconstruction is a distribution rather than a point estimate, and evaluation is driven by phase singularities computed from the Hilbert phase of the imputed signals.

What would settle it

Perform a study with simultaneous dense ground truth: record whole-atria activation with a high-density epicardial electrode array or optical mapping in the same heart while simulating 10% catheter coverage, then run FibMap; if the imputed rotor positions do not match the dense map with a phase-singularity true positive rate near the reported 0.89, the AcQMap-based validation has been measuring the wrong target.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that global AF dynamics are learnable from very sparse observations: a single model, trained with whole-atria supervision on simulated catheter paths, can impute the full atrial surface from only 10% coverage at any time. On the test set of unseen patients, FibMap achieves MAE 0.0574 and MSE 0.0069, versus 0.1205 and 0.0254 for matrix factorisation, and a phase-singularity true positive rate of 0.8924 versus 0.0803 for the next closest competitor. The model also outputs quantile predictions, so each imputed signal carries a confidence interval, and its sensitivity analysis shows reconstruction error falling with larger catheter area and shorter dwell time and rising for less organised (higher entropy) AF. In the three-patient clinical validation, the 99th percentile cross-correlation between FibMap imputation maps and non-contemporaneous AcQMap ground truth is 0.19-0.22 for the same patient, versus 0.16-0.17 for different patients and about 0.02 for spatiotemporally shuffled maps, which the authors take as evidence that FibMap recovers patient-specific atrial fibrillation dynamics rather than generic patterns.

Load-bearing premise

The load-bearing premise is that AcQMap's non-contact dipole-density recordings are a faithful ground truth for whole-atria AF dynamics; the paper itself cites evidence that non-contact mapping has low spatial resolution and can lead to incorrect interpretation of AF dynamics, so if AcQMap is unfaithful, the reported reconstruction errors do not measure true recovery of AF.

Editorial extensions

If this is right

  • Sequential contact mapping, already the standard clinical tool, could be upgraded to produce continuous global AF maps without additional hardware, since FibMap reconstructs the full atrium from 10% coverage.
  • Phase singularities are detected at 0.89 true positive rate, an 11-fold improvement over baselines, making rotor-guided ablation targeting testable with routinely collected data.
  • Per-patient fine-tuning takes about 22 minutes on a single GPU, so the procedure could fit inside a clinical mapping workflow.
  • The sensitivity analysis gives concrete protocol guidance: larger catheter surface area and shorter dwell time improve reconstruction, and patients with more organised AF are reconstructed more accurately; the model also flags uncertainty via wider quantile intervals at larger imputation horizons.
  • The learned state spaces and node embeddings organise patients by dominant frequency and Shannon entropy, offering a data-driven axis for electrophenotyping AF, though outcome validation is not part of this study.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: FibMap's confidence intervals could drive adaptive sampling, where the next catheter patch is chosen where predictive uncertainty is highest, potentially reducing the coverage needed for a target error.
  • Editorial inference: if entropy is a major determinant of reconstruction error, the same model could be used before a procedure to estimate how trustworthy the resulting FibMap map will be for a given patient.
  • Editorial inference: a stronger test of the clinical claim would be prospective and contemporaneous, recording contact and non-contact maps at the same moment and checking whether FibMap's imputed rotor positions predict ablation outcome; the present retrospective, non-contemporaneous comparison does not fully rule out that the correlation reflects shared patient-specific statistics rather than in
  • Editorial inference: if FibMap is right, it also offers a new instrument for basic arrhythmia science, a way to study rotor dynamics on the full atrial surface from data already collected, which could help settle disagreements about whether rotors are stable enough to ablate.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper introduces FibMap, a graph recurrent neural network that reconstructs whole-atrium atrial fibrillation dynamics from sparse sequential contact-mapping measurements. The model is trained on 51 persistent-AF patients with whole-atria AcQMap dipole-density recordings, then fine-tuned for each new patient using only the observed catheter patches. On a simulated test protocol with 10% surface coverage, FibMap reports a mean absolute error (MAE) of 0.0574 versus 0.1205 for matrix factorization, and a phase-singularity true positive rate of 0.8924 versus 0.0803 for the best baseline. The authors also present a clinical validation on three patients using EnSite HD Grid contact mapping, with cross-correlation analyses against non-contemporaneous AcQMap recordings, plus sensitivity analyses and visualisations of the learned state and embedding spaces.

Significance. If the central quantitative claims survive a corrected evaluation protocol, this is a useful contribution to computational cardiac electrophysiology: it formulates AF mapping as a graph-based spatiotemporal imputation problem, demonstrates the feasibility of reconstructing global dynamics from clinically realistic sparse measurements, and provides uncertainty estimates. The dataset of 51 whole-atria recordings is substantial for this domain, and the fine-tuning procedure is a practical approach to patient personalisation without retraining the full model. The main strengths are the problem formulation, the use of a real clinical dataset, and the clear presentation of the architectural components. However, the reported quantitative gains are currently weakened by a normalization protocol that leaks information from unobserved regions into the sparse inputs, by the absence of modern imputation baselines (notably the GRIN model on which FibMap is based), and by the reliance on AcQMap as ground truth despite the authors' own acknowledgement of its limited spatial resolution.

major comments (4)
  1. [S.3.1, S.3.4, Table 1] The normalization protocol leaks information from unobserved regions into the sparse inputs. Section S.3.1 states that signals are min-max normalised "across all nodes and times" before stratification, and the same global statistics are later applied to the test-set patches during fine-tuning and evaluation. Thus the observed patch inputs are scaled using the amplitude range of the unobserved (and in some cases future) portions of the atria, which is not available in clinical use. This can inflate the reported MAE of 0.0574 and the 2.1x improvement over matrix factorization. Please re-evaluate using normalization statistics computed from training data only, or from the observed patches at test time (e.g., patch-local min-max or z-scoring), and report whether the relative ranking and absolute metrics change.
  2. [Section 3, paragraph on AcQMap; Introduction paragraph on non-contact catheters] The paper uses AcQMap dipole-density maps as whole-atria ground truth for training and evaluation, yet it also cites Roney et al. [20] stating that non-contact mapping suffers from low spatial resolution and can lead to incorrect interpretation of AF dynamics. This makes the reported MAE and PS TPR measures of reconstruction fidelity to AcQMap-derived signals, not necessarily to true endocardial activation. The clinical validation does not resolve this because it also uses AcQMap as the comparator, and for only three patients with 99th-percentile cross-correlations of 0.19-0.22 against a shuffled baseline of 0.02. Please provide additional validation against a modality-independent reference (e.g., local contact electrograms acquired at the same sites) or explicitly scope the claims to reconstruction of AcQMap dipole-density signals rather than "true" AF dynamics.
  3. [Section 2.1, Table 1; S.3.6] The baseline set is too weak to support the claimed improvement. The comparison includes only Mean, matrix factorization, and univariate RNN/Bi-RNN models, with no modern imputation method and, crucially, no comparison against the base GRIN model [28] from which FibMap is derived. Without GRIN or another graph-based spatiotemporal imputer (e.g., BRITS, SAITS, CSDI), it is impossible to determine whether the reported 2.1x MAE improvement and 11.1x PS-TPR improvement arise from the added patient-specific embeddings and fine-tuning or simply from using a graph-based recurrent architecture. Please add GRIN as an ablation and at least one recent deep imputation baseline, and re-report Table 1.
  4. [Section 2.2, Figure 4] The claim of "reconstruction fidelity comparable to non-contact mapping" is not supported by the evidence presented. The intra-patient 99th-percentile cross-correlations of 0.19-0.22, while statistically separable from inter-patient (0.16-0.17) and shuffled (0.02) baselines, correspond to weak absolute agreement. With only three patients and a proxy metric based on phase signals from non-contemporaneous recordings, the abstract's statement that "clinical utility of FibMap is demonstrated" should be tempered to a proof-of-concept with limited statistical power. Please soften the wording and clearly state the sample size and the low absolute correlation magnitudes.
minor comments (5)
  1. [Abstract] The phrase "210% lower mean absolute error" is arithmetically incorrect; the result is a 2.1x improvement, which corresponds to roughly 52% lower error. Please rephrase to "2.1x lower" or "52% lower" both in the abstract and in any summary text.
  2. [Section 2.1] There is a typo: "an mean absolute error" should be "a mean absolute error".
  3. [S.3.3] The training procedure is described as "self-supervised," but the loss function in Eq. (16)-(18) uses whole-atria ground truth signals as targets; the stochastic masking is a data-augmentation scheme in a supervised setting. Please use the correct terminology (e.g., "supervised with random masking" rather than "self-supervised").
  4. [Table 1] The Mean baseline's PS TPR of 0.0126±0.0035 is trivially low for a constant imputation; it may help readers to note that Mean and MF are transductive and evaluated without any training on the test set, whereas FIBMAP and the RNN baselines are trained/fine-tuned, making the comparison not entirely like-for-like.
  5. [Section 2.3, Figure 5] The definition of "imputation horizon" in hops is given in the text but not operationalised in the figure or caption; please specify how the hop distance is computed from the spatiotemporal graph (e.g., the exact graph metric used) so that the horizontal axis in Figure 5B/C is reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the held-out whole-atria reconstruction targets are never used to fit the test-time parameters, and the only self-citations are architectural rather than load-bearing.

full rationale

The central claim of the paper is an empirical generalization result: FibMap is trained on whole-atria AcQMap supervision, then adapted to new patients by fine-tuning only patient-specific node and patient embeddings against an observed-patch reconstruction loss, and finally evaluated on the held-out unobserved regions against AcQMap ground truth (S.3.4 and S.3.5). The evaluation targets are therefore not used to fit the test-time parameters, so the headline MAE and PS TPR results are not forced by construction. The model architecture extends the GRNN framework of Cini et al. [28], a self-citation by co-authors, but that citation supplies a generic imputation building block, not the paper's validation or its reconstruction claim, and it is not used to forbid alternatives. The min-max normalization in S.3.1 uses whole-atrium statistics, which could leak global amplitude information into the sparse inputs and is a legitimate methodological concern, but it does not make the imputed dynamics equivalent to the observed inputs and applies equally to the baseline models; this belongs to correctness and robustness risk rather than circularity. No load-bearing step reduces to its own inputs, and no fitted parameter is renamed as a prediction. Score 0.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The free parameters are data-processing choices and evaluation thresholds that materially affect the reported numbers. The axioms capture the modeling and measurement assumptions on which the central claim rests, most importantly the validity of AcQMap as ground truth.

free parameters (5)
  • Graph node count = 500
    Whole-atria recordings are resampled to 500 nodes via k-means; this resolution is a hand-chosen trade-off and affects the graph structure and reconstruction error.
  • Temporal sampling rate = 70 Hz
    Signals are low-pass filtered and downsampled to 70 Hz; temporal resolution affects the reconstruction and phase singularity detection.
  • Main test catheter configuration = 10% area, 1 s dwell time, 0 overlap
    The headline result uses this specific simulated catheter configuration; sensitivity analysis shows performance varies with these parameters.
  • PS detection tolerance = 0.1 s, 4-hop neighborhood
    The true positive rate for phase singularities is defined by these tolerance thresholds; different tolerances would change TPR.
  • Fine-tuning learning rate and batch size = lr=0.005, batch=16
    Chosen via validation on the held-out validation set; affects adaptation to new patients.
assumptions (5)
  • domain assumption AcQMap dipole density maps accurately represent whole-atria AF electrical activity
    Used as ground truth for training and all evaluations; the paper acknowledges non-contact mapping limitations but relies on it.
  • domain assumption AF dynamics can be modeled as coupled oscillators on a fixed graph derived from the atrial mesh
    Underpins the graph neural network formulation (Section 1, S.2.1).
  • domain assumption Simulated self-avoiding catheter walks replicate routine clinical sequential contact mapping
    The primary evaluation uses simulated sparse masks; if real catheter movement differs, the performance estimates may not transfer (Section 2.1, S.3.2).
  • domain assumption Phase singularities in reconstructed phase maps are meaningful markers of AF drivers and can be manually identified with acceptable inter-observer agreement
    The PS TPR is a headline metric, based on manual annotation of 1-second segments (Section 2.1, S.3.5).
  • domain assumption Min-max normalization and spatial/temporal resampling preserve the spatiotemporal patterns of interest
    All signals are normalized to [0,1] before computing MAE; the metric is relative to this normalization (S.3.1).

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Cite this review

Pith. "Pith review of Learning to Predict Global Atrial Fibrillation Dynamics from Sparse Measurements." pith.science (2026). https://pith.science/paper/ZHJNBLLX

@misc{pith2026250209473,
  author       = {Pith},
  title        = {Pith review of: Learning to Predict Global Atrial Fibrillation Dynamics from Sparse Measurements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZHJNBLLX}},
  note         = {Machine review of arXiv:2502.09473}
}
read the original abstract

Catheter ablation of Atrial Fibrillation (AF) consists of a one-size-fits-all treatment with limited success in persistent AF. This may be due to our inability to map the dynamics of AF with the limited resolution and coverage provided by sequential contact mapping catheters, preventing effective patient phenotyping for personalised, targeted ablation. Here we introduce FibMap, a graph recurrent neural network model that reconstructs global AF dynamics from sparse measurements. Trained and validated on 51 non-contact whole atria recordings, FibMap reconstructs whole atria dynamics from 10% surface coverage, achieving a 210% lower mean absolute error and an order of magnitude higher performance in tracking phase singularities compared to baseline methods. Clinical utility of FibMap is demonstrated on real-world contact mapping recordings, achieving reconstruction fidelity comparable to non-contact mapping. FibMap's state-spaces and patient-specific parameters offer insights for electrophenotyping AF. Integrating FibMap into clinical practice could enable personalised AF care and improve outcomes.

Figures

Figures reproduced from arXiv: 2502.09473 by the authors.

Figure 1
Figure 1. The inputs (A) and architecture (B) of FIBMAP. A) The atrium is discretised into nodes and edges via a triangulated mesh, and from this the graph adjacency matrix (describing the coupling between nodes) and the observed time series are derived. The patient-specific parameters (node and patient embeddings) are also provided as input to personalise FIBMAP’s imputation maps. B) FIBMAP is instantiated as a bidirectional… view at source ↗
Figure 2
Figure 2. Quantitative results of FIBMAP imputation mapping. A) Reconstruction loss as a function of the number of epochs for the fine-tuning of FIBMAP on the validation set, with a strong correlation of r = 0.97 (p < 0.0001) present between the loss curves of the observed patch and whole atria. B) Test set reconstruction performance of all models quantified using the mean absolute error (MAE) across all space and time. C) Te… view at source ↗
Figure 3
Figure 3. Qualitative results of FIBMAP imputation mapping. A) Snapshots of the imputation maps of FIBMAP and MF, versus the ground truth AcQMap phase maps for two different patients (rows). FIBMAP imputes the missing signals (grey regions) from sparse observations (10% of atria) of AcQMap recordings with a simulated sequential contact mapping multipolar catheter (surface area of 10%, no spatial overlap and 1 second dwell tim… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Validation of FIBMAP imputation maps from EnSite Precision HD Grid Mapping against non￾contemporaneous ground truth AcQMap recordings. A) Sliding window cross-correlation analysis between AcQMap and FIBMAP phase signals, enabling comparison between non-contemporaneous …
Figure 5
Figure 5. Figure 5: Results of FIBMAP sensitivity analysis. A) MAE of FIBMAP reconstructions as a function of catheter surface area, dwell time and entropy (left vs. right). B) Reconstruction MAE of FIBMAP and the predicted confidence intervals as a function of imputation horizon. intra-p…
Figure 6
Figure 6. Figure 6: Interpretation of FIBMAP hidden state and patient-specific node parameters. Ai) Trajectory of the hidden state of a node in the test set, where the state space has been reduced to 3D using t-SNE dimensionality reduction. Trajectories are coloured by their position in t…

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Reference graph

Works this paper leans on

72 extracted references · 68 canonical work pages

  1. [20]

    Spatial resolution requirements for accurate identification of drivers of atrial fibrillation

    Caroline H. Roney et al. “Spatial resolution requirements for accurate identification of drivers of atrial fibrillation”.Circulation: Arrhythmia and Electrophysiology 10.5 (2017), e004899

  2. [28]

    Filling the g_ap_s: Multivariate time series imputation by graph neural networks

    Andrea Cini, Ivan Marisca, and Cesare Alippi. “Filling the g_ap_s: Multivariate time series imputation by graph neural networks”. Proceedings of the International Conference on Learning Representations (2022)

  3. [1]

    Lifetime risk of atrial fibrillation by race and socioeconomic status: ARIC study (Atherosclerosis Risk in Communities)

    Liping Mou et al. “Lifetime risk of atrial fibrillation by race and socioeconomic status: ARIC study (Atherosclerosis Risk in Communities)”. Circulation: Arrhythmia and Electrophysiology 11.7 (2018), e006350

  4. [2]

    Global epidemiology of atrial fibrillation: An increasing epidemic and public health challenge

    Giuseppe Lippi, Fabian Sanchis-Gomar, and Gianfranco Cervellin. “Global epidemiology of atrial fibrillation: An increasing epidemic and public health challenge”. International Journal of Stroke 16.2 (2021), pp. 217–221

  5. [3]

    Stroke prevention in atrial fibrillation: Looking forward

    Aristeidis H. Katsanos, Hooman Kamel, Jeff S. Healey, and Robert G. Hart. “Stroke prevention in atrial fibrillation: Looking forward”. Circulation 142.24 (2020), pp. 2371–2388

  6. [4]

    Atrial fibrillation in heart failure: Epidemiology, pathophysiology, and rationale for therapy

    William H. Maisel and Lynne Warner Stevenson. “Atrial fibrillation in heart failure: Epidemiology, pathophysiology, and rationale for therapy”. The American Journal of Cardiology 91.6 (2003), pp. 2–8

  7. [5]

    Impact of atrial fibrillation on mortality, stroke, and medical costs

    Philip A. Wolf, Janet B. Mitchell, Colin S. Baker, William B. Kannel, and Ralph B. D’Agostino. “Impact of atrial fibrillation on mortality, stroke, and medical costs”. Archives of Internal Medicine 158.3 (1998), pp. 229–234

  8. [6]

    Cost of an emerging epidemic: An economic analysis of atrial fibrillation in the UK

    S Stewart, N Murphy, A Walker, A McGuire, and J J V McMurray. “Cost of an emerging epidemic: An economic analysis of atrial fibrillation in the UK”. Heart 90.3 (2004), pp. 286–292

Show all 72 references
  1. [7]

    Atrial fibrillation burden and clinical outcomes in heart failure: The CASTLE-AF trial

    Johannes Brachmann et al. “Atrial fibrillation burden and clinical outcomes in heart failure: The CASTLE-AF trial”. Clinical Electrophysiology 7.5 (2021), pp. 594–603

  2. [8]

    Luigi Di Biase et al. “Ablation versus amiodarone for treatment of persistent atrial fibrillation in patients with congestive heart failure and an implanted device: Results from the AATAC multicenter randomized trial”.Circulation 133.17 (2016), pp. 1637–1644. 10 Learning to Pr...

  3. [9]

    Cryoballoon or radiofrequency ablation for paroxysmal atrial fibrillation

    Karl-Heinz Kuck et al. “Cryoballoon or radiofrequency ablation for paroxysmal atrial fibrillation”. New England Journal of Medicine 374.23 (2016), pp. 2235–2245

  4. [10]

    Five-year outcome of catheter ablation of persistent atrial fibrillation using termination of atrial fibrillation as a procedural endpoint

    Daniel Scherr et al. “Five-year outcome of catheter ablation of persistent atrial fibrillation using termination of atrial fibrillation as a procedural endpoint”. Circulation: Arrhythmia and Electrophysiology 8.1 (2015), pp. 18–24

  5. [11]

    The electrical isolation of the left atrial posterior wall in catheter ablation of persistent atrial fibrillation

    Jung Myung Lee et al. “The electrical isolation of the left atrial posterior wall in catheter ablation of persistent atrial fibrillation”. Clinical Electrophysiology 5.11 (2019), pp. 1253–1261

  6. [12]

    Approaches to catheter ablation for persistent atrial fibrillation

    Atul Verma et al. “Approaches to catheter ablation for persistent atrial fibrillation”. New England Journal of Medicine 372.19 (2015), pp. 1812–1822

  7. [13]

    Pulmonary vein isolation versus defragmentation: The CHASE-AF clinical trial

    Julia V ogler et al. “Pulmonary vein isolation versus defragmentation: The CHASE-AF clinical trial”.Journal of the American College of Cardiology 66.24 (2015), pp. 2743–2752

  8. [14]

    Narayan et al

    Sanjiv M. Narayan et al. “Treatment of atrial fibrillation by the ablation of localized sources: CONFIRM (Conventional Ablation for Atrial Fibrillation With or Without Focal Impulse and Rotor Modulation) trial”. Journal of the American College of Cardiology 60.7 (2012), pp. 628–636

  9. [15]

    No benefit of complex fractionated atrial electrogram ablation in addition to circumferential pulmonary vein ablation and linear ablation: Benefit of complex ablation study

    Kelvin CK Wong et al. “No benefit of complex fractionated atrial electrogram ablation in addition to circumferential pulmonary vein ablation and linear ablation: Benefit of complex ablation study”. Circulation: Arrhythmia and Electrophysiology 8.6 (2015), pp. 1316–1324

  10. [16]

    Toward mechanism-directed electrophenotype-based treatments for atrial fibrillation

    Fu Siong Ng, Balvinder S. Handa, Xinyang Li, and Nicholas S. Peters. “Toward mechanism-directed electrophenotype-based treatments for atrial fibrillation”. Frontiers in Physiology 11 (2020)

  11. [17]

    High-density and high coverage composite mapping of repetitive atrial activation patterns

    Ozan Özgül et al. “High-density and high coverage composite mapping of repetitive atrial activation patterns”. Computers in Biology and Medicine 159 (2023), p. 106920

  12. [18]

    Long-term clinical outcomes of focal impulse and rotor modulation for treatment of atrial fibrillation: A multicenter experience

    Eric Buch et al. “Long-term clinical outcomes of focal impulse and rotor modulation for treatment of atrial fibrillation: A multicenter experience”. Heart Rhythm 13.3 (2016), pp. 636–641

  13. [19]

    Noninvasive electrocardiographic imaging

    Yoram Rudy Ph.D. and John E. Burnes M.S. “Noninvasive electrocardiographic imaging”.Annals of Noninvasive Electrocar- diology 4.3 (1999), pp. 340–359

  14. [21]

    Synchronization of pulse-coupled biological oscillators

    Renato E. Mirollo and Steven H. Strogatz. “Synchronization of pulse-coupled biological oscillators”. SIAM Journal on Applied Mathematics 50.6 (1990), pp. 1645–1662

  15. [22]

    The fundamental organization of cardiac mitochondria as a network of coupled oscillators

    Miguel Antonio Aon, Sonia Cortassa, and Brian O’Rourke. “The fundamental organization of cardiac mitochondria as a network of coupled oscillators”. Biophysical Journal 91.11 (2006), pp. 4317–4327

  16. [23]

    Nonlinear and stochastic dynamics in the heart

    Zhilin Qu, Gang Hu, Alan Garfinkel, and James N. Weiss. “Nonlinear and stochastic dynamics in the heart”. Physics Reports 543.2 (2014), pp. 61–162

  17. [24]

    The graph neural network model

    Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini. “The graph neural network model”. IEEE Transactions on Neural Networks 20.1 (2008), pp. 61–80

  18. [25]

    Geometric deep learning: Going beyond Euclidean data

    Michael M. Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst. “Geometric deep learning: Going beyond Euclidean data”. IEEE Signal Processing Magazine 34.4 (2017), pp. 18–42

  19. [26]

    A gentle introduction to deep learning for graphs

    Davide Bacciu, Federico Errica, Alessio Micheli, and Marco Podda. “A gentle introduction to deep learning for graphs”. Neural Networks 129 (2020), pp. 203–221

  20. [27]

    Structured sequence modeling with graph convolutional recurrent networks

    Youngjoo Seo, Michaël Defferrard, Pierre Vandergheynst, and Xavier Bresson. “Structured sequence modeling with graph convolutional recurrent networks”. Proceedings of the 25th International Conference on Neural Information Processing. Springer, 2018, pp. 362–373

  21. [29]

    Word embedding for understanding natural language: A survey

    Yang Li and Tao Yang. “Word embedding for understanding natural language: A survey”.Guide to Big Data Applications (2018), pp. 83–104

  22. [30]

    Natasja MS De Groot et al. “Critical appraisal of technologies to assess electrical activity during atrial fibrillation: A position paper from the European heart rhythm association and European society of cardiology working group on eCardiology in collaboration with the heart ...

  23. [31]

    Validation of dipole density mapping during atrial fibrillation and sinus rhythm in human left atrium

    Rui Shi et al. “Validation of dipole density mapping during atrial fibrillation and sinus rhythm in human left atrium”. Clinical Electrophysiology 6.2 (2020), pp. 171–181

  24. [32]

    Standardised framework for quantitative analysis of fibrillation dynamics

    Xinyang Li et al. “Standardised framework for quantitative analysis of fibrillation dynamics”. Scientific Reports 9.1 (2019), p. 16671

  25. [33]

    Visualizing data using t-SNE

    Laurens Van der Maaten and Geoffrey Hinton. “Visualizing data using t-SNE.”Journal of Machine Learning Research 9.11 (2008)

  26. [34]

    Recurrence plots for the analysis of complex systems

    Norbert Marwan, M Carmen Romano, Marco Thiel, and Jurgen Kurths. “Recurrence plots for the analysis of complex systems”. Physics Reports 438.5-6 (2007), pp. 237–329

  27. [35]

    V ortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation

    Flavio Fenton and Alain Karma. “V ortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation”. Chaos: An Interdisciplinary Journal of Nonlinear Science 8.1 (1998), pp. 20–47. 11 Learning to Predict Global Atrial Fibrill...

  28. [36]

    Models of cardiac tissue electrophysiology: Progress, challenges and open questions

    R. H. Clayton et al. “Models of cardiac tissue electrophysiology: Progress, challenges and open questions”. Progress in Biophysics and Molecular Biology 104.1-3 (2011), pp. 22–48

  29. [37]

    Graph-based time series clustering for end-to-end hierarchical forecasting

    Andrea Cini, Danilo Mandic, and Cesare Alippi. “Graph-based time series clustering for end-to-end hierarchical forecasting”. Proceedings of the 41st International Conference on Machine Learning (2024)

  30. [38]

    Learning to reconstruct missing data from spatiotemporal graphs with sparse observations

    Ivan Marisca, Andrea Cini, and Cesare Alippi. “Learning to reconstruct missing data from spatiotemporal graphs with sparse observations”. Proceedings of the 36th International Conference on Neural Information Processing Systems(2022), pp. 32069–32082

  31. [39]

    Graph signal processing: Overview, challenges, and applications

    Antonio Ortega, Pascal Frossard, Jelena Kovaˇcevi´c, José M. F. Moura, and Pierre Vandergheynst. “Graph signal processing: Overview, challenges, and applications”. Proceedings of the IEEE 106.5 (2018), pp. 808–828

  32. [40]

    Data analytics on graphs. Part II: Signals on graphs

    Ljubiša Stankovi´c et al. “Data analytics on graphs. Part II: Signals on graphs”.Foundations and Trends® in Machine Learning 13.2-3 (2020), pp. 158–331. ISSN : 1935-8237

  33. [41]

    Data analytics on graphs. Part III: Machine learning on graphs, from graph topology to applications

    Ljubiša Stankovi´c et al. “Data analytics on graphs. Part III: Machine learning on graphs, from graph topology to applications”. Foundations and Trends® in Machine Learning13.4 (2020), pp. 332–530. ISSN : 1935-8237

  34. [42]

    Semi-supervised classification with graph convolutional networks

    Thomas N. Kipf and Max Welling. “Semi-supervised classification with graph convolutional networks”.Proceedings of the International Conference on Learning Representations (2017)

  35. [43]

    Deep learning on graphs: A survey

    Ziwei Zhang, Peng Cui, and Wenwu Zhu. “Deep learning on graphs: A survey”. IEEE Transactions on Knowledge and Data Engineering 34.1 (2020), pp. 249–270

  36. [44]

    Graph deep learning for time series forecasting

    Andrea Cini, Ivan Marisca, Daniele Zambon, and Cesare Alippi. “Graph deep learning for time series forecasting”. arXiv preprint arXiv:2310.15978 (2023)

  37. [45]

    A survey on graph neural networks for time series: Forecasting, classification, imputation, and anomaly detection

    Ming Jin et al. “A survey on graph neural networks for time series: Forecasting, classification, imputation, and anomaly detection”. IEEE Transactions on Pattern Analysis and Machine Intelligence(2024)

  38. [46]

    On the equivalence between temporal and static equivariant graph representations

    Jianfei Gao and Bruno Ribeiro. “On the equivalence between temporal and static equivariant graph representations”. Proceedings of the 39th International Conference on Machine Learning (2022), pp. 7052–7076

  39. [47]

    Scalable spatiotemporal graph neural networks

    Andrea Cini, Ivan Marisca, Filippo Maria Bianchi, and Cesare Alippi. “Scalable spatiotemporal graph neural networks”. Proceedings of the AAAI Conference on Artificial Intelligence. V ol. 37. 2023. Chap. 6, pp. 7218–7226

  40. [48]

    Diffusion convolutional recurrent neural network: Data-driven traffic forecasting

    Yaguang Li, Rose Yu, Cyrus Shahabi, and Yan Liu. “Diffusion convolutional recurrent neural network: Data-driven traffic forecasting”. Proceedings of the International Conference on Learning Representations (2018)

  41. [49]

    Graph neural network for traffic forecasting: A survey

    Weiwei Jiang and Jiayun Luo. “Graph neural network for traffic forecasting: A survey”.Expert Systems with Applications 207 (2022), p. 117921

  42. [50]

    Learning skillful medium-range global weather forecasting

    Remi Lam et al. “Learning skillful medium-range global weather forecasting”. Science 382.6677 (2023), pp. 1416–1421

  43. [51]

    Taming local effects in graph-based spatiotemporal forecasting

    Andrea Cini, Ivan Marisca, Daniele Zambon, and Cesare Alippi. “Taming local effects in graph-based spatiotemporal forecasting”. Proceedings of the 37th International Conference on Neural Information Processing Systems36 (2024)

  44. [52]

    NodeTrans: A graph transfer learning approach for traffic prediction

    Xueyan Yin, Feifan Li, Yanming Shen, Heng Qi, and Baocai Yin. “NodeTrans: A graph transfer learning approach for traffic prediction”. arXiv preprint arXiv:2207.01301 (2022)

  45. [53]

    Bayesian probabilistic matrix factorization using Markov chain Monte Carlo

    Ruslan Salakhutdinov and Andriy Mnih. “Bayesian probabilistic matrix factorization using Markov chain Monte Carlo”. Proceedings of the 25th International Conference on Machine Learning. 2008, pp. 880–887

  46. [54]

    Algorithms for non-negative matrix factorization

    Daniel Lee and H Sebastian Seung. “Algorithms for non-negative matrix factorization”.Proceedings of the 13th International Conference on Neural Information Processing Systems 13 (2000)

  47. [55]

    Graph regularized nonnegative matrix factorization for data representation

    Deng Cai, Xiaofei He, Jiawei Han, and Thomas S Huang. “Graph regularized nonnegative matrix factorization for data representation”. IEEE Transactions on Pattern Analysis and Machine Intelligence33.8 (2010), pp. 1548–1560

  48. [56]

    Temporal regularized matrix factorization for high-dimensional time series prediction

    Hsiang-Fu Yu, Nikhil Rao, and Inderjit S Dhillon. “Temporal regularized matrix factorization for high-dimensional time series prediction”. Proceedings of the 30th International Conference on Neural Information Processing Systems29 (2016)

  49. [57]

    BRITS: Bidirectional recurrent imputation for time series

    Wei Cao et al. “BRITS: Bidirectional recurrent imputation for time series”.Proceedings of the 32nd International Conference on Neural Information Processing Systems 31 (2018)

  50. [58]

    Time-series generative adversarial networks

    Jinsung Yoon, Daniel Jarrett, and Mihaela Van der Schaar. “Time-series generative adversarial networks”.Proceedings of the 33rd International Conference on Neural Information Processing Systems32 (2019)

  51. [59]

    NAOMI: Non-autoregressive multiresolution sequence imputation

    Yukai Liu, Rose Yu, Stephan Zheng, Eric Zhan, and Yisong Yue. “NAOMI: Non-autoregressive multiresolution sequence imputation”. Proceedings of the 33rd International Conference on Neural Information Processing Systems32 (2019)

  52. [60]

    SAITS: Self-attention-based imputation for time series

    Wenjie Du, David Côté, and Yan Liu. “SAITS: Self-attention-based imputation for time series”. Expert Systems with Applications 219 (2023), p. 119619

  53. [61]

    CSDI: Conditional score-based diffusion models for probabilistic time series imputation

    Yusuke Tashiro, Jiaming Song, Yang Song, and Stefano Ermon. “CSDI: Conditional score-based diffusion models for probabilistic time series imputation”. Proceedings of the 35th International Conference on Neural Information Processing Systems 34 (2021), pp. 24804–24816

  54. [62]

    Diffusion-based time series imputation and forecasting with structured state space models

    J Alcaraz and N Strodthoff. “Diffusion-based time series imputation and forecasting with structured state space models”. Transactions on Machine Learning Research(2023)

  55. [63]

    Improving diffusion models for ECG imputation with an augmented template prior

    Alexander Jenkins, Zehua Chen, Fu Siong Ng, and Danilo Mandic. “Improving diffusion models for ECG imputation with an augmented template prior”. arXiv preprint arXiv:2310.15742 (2023)

  56. [64]

    Principles and algorithms for forecasting groups of time series: Locality and globality

    Pablo Montero-Manso and Rob J Hyndman. “Principles and algorithms for forecasting groups of time series: Locality and globality”. International Journal of Forecasting37.4 (2021), pp. 1632–1653. 12 Learning to Predict Global Atrial Fibrillation Dynamics from Sparse Measurements...

  57. [65]

    Residual gated graph convnets

    Xavier Bresson and Thomas Laurent. “Residual gated graph convnets”. arXiv preprint arXiv:1711.07553 (2017)

  58. [66]

    Diffusion-convolutional neural networks

    James Atwood and Don Towsley. “Diffusion-convolutional neural networks”.Proceedings of the 30th International Confer- ence on Neural Information Processing Systems 29 (2016)

  59. [67]

    Quantile regression

    Roger Koenker and Kevin F Hallock. “Quantile regression”. Journal of Economic Perspectives 15.4 (2001), pp. 143–156

  60. [68]

    Laplacian eigenmaps for dimensionality reduction and data representation

    Mikhail Belkin and Partha Niyogi. “Laplacian eigenmaps for dimensionality reduction and data representation”. Neural Computation 15.6 (2003), pp. 1373–1396

  61. [69]

    Method for registration of 3-D shapes

    Paul J Besl and Neil D McKay. “Method for registration of 3-D shapes”. Proceedings of Sensor fusion IV: Control Paradigms and Data Structures 1611 (1992), pp. 586–606. 13 Learning to Predict Global Atrial Fibrillation Dynamics from Sparse Measurements A PREPRINT Supplementary ...

  62. [70]

    Mean, which performs imputation using the node-level average

  63. [71]

    Univariate RNN, which performs imputation based solely on the node-level signals

  64. [72]

    Mean and MF baseline models are employed solely on the test set due to their transductive nature

    Univariate bidirectional (Bi)-RNN. Mean and MF baseline models are employed solely on the test set due to their transductive nature. Both the univariate RNN and Bi-RNN models were trained using MAE loss function and followed identical hyperparameter settings and training-test ...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.