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Abstract
High-fidelity cardiac electrophysiology (EP) simulations are critical for understanding and treating heart disease, but conventional solvers are often too slow for real-time applications. Recent deep learning approaches have explored physics-informed neural networks as surrogate models to accelerate EP prediction while preserving biophysical fidelity. However, these methods typically struggle to incorporate key anatomical features, such as cardiac geometry and fiber orientation, and lack explicit integration of EP-specific physical constraints, limiting their reliability and interpretability. In this study, we present a physics-informed graph attention network that serves as an efficient surrogate model for cardiac EP. By embedding the monodomain equation and Aliev–Panfilov ionic model into the loss function and leveraging graph attention mechanisms to capture anatomical structure from cardiac meshes, our approach sub- stantially outperforms methods that disregard fiber architecture. Exper- iments on unseen 3D biventricular geometries demonstrate strong gen- eralization and accurate wavefront dynamics without fine-tuning, estab- lishing our method as a promising surrogate for anatomically faithful, real-time EP modeling
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/4252_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
N/A
Link to the Dataset(s)
N/A
BibTex
@InProceedings{TraVu_PhysicsInformed_MICCAI2026,
author = { Tran, Vu Anh AND Wang, Mengxiao AND Lyu, Yilin AND Chauhan, Jagmohan AND Muthurangu, Vivek AND Sia, Ching-Hui AND Li, Lei},
title = { { Physics-Informed Surrogate Model Using Graph Neural Network for Cardiac Electrophysiology } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16896},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
The author proposed a physics-informed GNN model for cardiac electrophysiology. The biventricular mesh was formulated as a graph input, with anatomical features such as fibre orientation and inter-node distance included as edge attributes, while the action potential at each time point was used as node features.
The proposed GNN-based model uses four history frames and predicts increment values for the activation potential and recovery variables in the subsequent frame. This allow the incorporation the electrophysiology model equations as PDE and ODE loss terms during optimisation.
The model was trained and tested on simulated data generated using the Aliev–Panfilov model. The results showed that the model achieved better performance than existing methods without the additional physics constraints and cardiac geometry information.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
- The author proposes a novel approach for integrating biventricular anatomy and geometry with physics-informed constraints, and demonstrates that the method outperforms existing surrogate models.
- The model is shown to be effective compared with the baseline model and is able to faithfully reproduce wavefront propagation with lower computational cost than traditional solvers.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
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The evaluation is limited to simulated data. Although the Aliev–Panfilov model has been shown to approximate EP wavefront propagation effectively, it remains a simplified model. Similarly, the generation of the fiber and purkinje tree is also simplified. As a result, it is difficult to draw firm conclusions about how the model would perform on real patient electrical propagation.
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The author does not provide sufficient detail on the optimisation of the baseline model. What were the training conditions for the baseline data-driven model? Was the model retrained on the newly generated dataset from this work? According to the cited reference, AGATA was originally used in a different configuration, including the EP simulation model, voltage range, graph input, and presence of scar regions. Additional details on how the baseline model was optimised would help the reader interpret the comparison. The use of LeakyReLU activation in AGATA may also affect performance when training and inferring on inputs with a negative voltage range.
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The author does not provide sufficient computational details. Since the one of the goals of this work is to develop a surrogate model to reduce computation time, more details on the compuation ressources and time differences between the FEM solvers and baseline model, would provide more supporting evidence for the proposed method.
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- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
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The evaluation is limited to simulated data. Although the Aliev–Panfilov model has been shown to approximate EP wavefront propagation effectively, it remains a simplified model. Similarly, the generation of the fiber and purkinje tree is also simplified. As a result, it is difficult to draw firm conclusions about how the model would perform on real patient electrical propagation.
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The author does not provide sufficient detail on the optimisation of the baseline model. What were the training conditions for the baseline data-driven model? Was the model retrained on the newly generated dataset from this work? According to the cited reference, AGATA was originally used in a different configuration, including the EP simulation model, voltage range, graph input, and presence of scar regions. Additional details on how the baseline model was optimised would help the reader interpret the comparison. The use of LeakyReLU activation in AGATA may also affect performance when training and inferring on inputs with a negative voltage range.
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The author does not provide sufficient computational details. Since the one of the goals of this work is to develop a surrogate model to reduce computation time, more details on the compuation ressources and time differences between the FEM solvers and baseline model, would provide more supporting evidence for the proposed method.
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- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
The model itself is very strong. The author proposes a novel method for integrating geometric information and physical formulation into the surrogate model. Nevertheless, I would strongly encourage the author to be more cautious with some of the claims, particularly those regarding the state-of-the-art comparison.
Review #2
- Please describe the contribution of the paper
This paper presents a physics-informed graph neural network as a surrogate model for cardiac electrophysiology simulation. By jointly incorporating cardiac geometry, fiber orientation, and reaction-diffusion physics constraints into a spatiotemporal GNN framework, the model achieves real-time and accurate electrical wave propagation prediction on unseen biventricular geometries, offering a compelling alternative to conventional finite element solvers.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.Through careful design of the graph data representation and GNN architecture, the model effectively encodes cardiac geometry and fiber orientation, enabling generalization across unseen biventricular meshes with varying shapes and resolutions. 2.By embedding the monodomain equation and Aliev-Panfilov ionic model directly into the training loss, the model enforces biophysical consistency during training, leading to more physically plausible predictions compared to purely data-driven baselines. 3.The adoption of multi-step rollout training with gradual teacher forcing reduction mitigates error accumulation during autoregressive inference, improving model stability over longer prediction horizons.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1.The paper contains several undefined or ambiguous symbols. For instance, I_stim in Equation 3 and the interior node set I in Equation 7 are introduced without explicit definition. More notably, the relationship between the action potential Vm and the normalized transmembrane potential u is never clarified, despite them appearing to represent the same variable based on Equation 7.The authors should have explicitly established this equivalence rather than leaving it to the reader to infer. 2.Several important experimental details are missing. The number of mesh nodes is never reported, making it difficult to assess the true computational cost of the approach. Training a physics-informed model across 130 diverse geometries is likely non-trivial in terms of training cost. Even if inference is fast, high training cost could constitute a practical limitation that the paper does not adequately address. 3.The choice of T=4 history frames and a 4-step rollout during training is overly conservative and insufficiently justified. Given that cardiac depolarization typically spans several hundred milliseconds, training within a mere 16ms window raises concerns about whether the model can capture meaningful long-term electrophysiological dynamics. This limited temporal scope during training likely contributes to the observed performance degradation at longer prediction horizons, yet no ablation study is provided to validate or motivate this design choice.
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper presents a well-motivated and clearly described framework that jointly incorporates cardiac geometry, fiber orientation, and explicit physics constraints into a spatiotemporal GNN. However, the experimental section contains notable gaps, including missing mesh and training cost details, that raise concerns about practical feasibility. The choice of T=4 and 4-step rollout covering only 16ms is difficult to justify for a system targeting predictions over several hundred milliseconds, with no ablation study provided to support this decision. I would like to see the authors address these points in the rebuttal.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #3
- Please describe the contribution of the paper
This paper presents a physics-informed spatio-temporal GNN surrogate for fast cardiac electrophysiology simulation. The model takes a biventricular mesh as graph input, explicitly encodes fiber, sheet, and normal directions together with anisotropic conduction features, and is trained with residual constraints derived from the monodomain PDE and the Aliev-Panfilov ODE. It is then used for autoregressive wavefront propagation prediction and activation time estimation on unseen 3D geometries.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.The problem setting is practically relevant. In contrast to prior cardiac EP surrogates evaluated only on regular grids, idealized slabs, or low-dimensional geometries, this work targets realistic 3D biventricular meshes and directly incorporates anatomical anisotropy, including fiber, sheet, and normal directions, into the graph representation. This is well aligned with the requirements of cardiac digital twins. 2.The method is also reasonably well matched to the task. The authors not only process mesh-based EP data using GNN, but also explicitly write the residuals of monodomain diffusion and Aliev–Panfilov reaction into the training objective, and approximate the discrete diffusion operator using RBF-FD. Compared to the surrogate that only does data fitting, this design is more in line with the mechanism structure of cardiac EP. 3.The experiments also reflect two sensible forms of generalization. The train, validation, and test sets are split by geometry or trajectory, which helps avoid leakage from the same mesh. The authors also evaluate on unseen geometries with different resolutions and provide a rollout visualization on a higher-resolution mesh, which is closer to practical application than only conducting tests within the same distribution.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1.The experimental comparison remains limited, so the claim of superiority over existing methods is not yet fully supported. In the current version, the clearest comparison is between the physics-informed model and its own data-driven variant. Although AGATA is mentioned as an external baseline, the paper does not clearly describe its input setting, whether it uses the same geometric or fiber information, or whether the training and evaluation protocol is fully aligned. As a result, the current evidence is sufficient to show that the physics-informed loss is helpful, but not sufficient to establish a broader advantage over existing cardiac EP surrogates. 2.Generalization across different mesh resolutions and realistic geometries is important. Although the authors mentioned that the test set contains different resolutions and presented the results on a higher-resolution grid, they did not provide a systematic statistics stratified by resolution or geometry complexity, so it is still impossible to determine whether the model truly has stable cross-resolution generalization, rather than being only effective in similar distributions. 3.There are obvious unclear points in the writing and presentation of the results, which affect readability and credibility. For example, the title of Table 1 is called “activation time map prediction”, but the table lists the RMSE/MAE/PCC of Vm and “Sv”; meanwhile, “Sv” is not clearly defined in the method section. The RMSE in the table (Vm) lacks a right parenthesis. Such inconsistencies in symbols and task definitions make it difficult for readers to accurately understand the evaluated object. 4.The argument for the speed advantage is not sufficiently clear. The paper provides an average inference time of 0.128 seconds. However, the hardware and corresponding mesh size used by the method used in this paper, the FEM solver, and the external baseline AGATA, as well as the details of the evaluation protocol, were not clearly explained.
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
I rated this paper as a weak accept because it addresses an important and clinically relevant problem, and the proposed method is technically sound. At the same time, the empirical validation and the presentation are not yet strong enough to justify a confident acceptance.
The main strength of the paper is that it moves beyond idealized cardiac EP settings and studies a physics-informed surrogate on realistic 3D biventricular meshes with explicit anatomical anisotropy. This is a meaningful direction for cardiac digital twins. And the method to be well aligned with the problem. The combination of a spatio-temporal GNN with explicit monodomain and Aliev–Panfilov residual constraints is more convincing than a purely data-driven surrogate, and the geometry-based train, validation, and test split is a reasonable design choice that helps reduce leakage.
My reservation is mainly due to four issues. The comparison to prior work is too limited to support a strong claim of superiority, and the clearest result at present is that the physics-informed model outperforms its own data-driven counterpart. The paper also claims generalization across resolutions and geometries, but does not provide a systematic stratified analysis to substantiate this point. In addition, several inconsistencies in the metrics and notation weaken confidence in the reported results. Finally, the efficiency claim is difficult to assess because the experimental details are not sufficiently specified. A strong rebuttal that addresses these concerns would increase my confidence in the paper.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
I am inclined to recommend acceptance. The rebuttal addresses several important concerns raised by the reviewers, including mesh size, training cost, hardware setup, inference speed, variable definitions, and the choice of temporal window length. These clarifications make the experimental setup easier to assess and address my earlier concerns about unclear presentation and insufficient support for the efficiency claim.
Some limitations remain. The comparison with AGATA is still not fully rigorous, since the authors did not reproduce the method and only used the activation-time MAE from the original paper as a reference. The paper should therefore avoid making a strong claim of overall superiority over existing methods. The evidence for cross-resolution generalization is also still limited. The rebuttal mainly provides a mechanistic explanation and a small amount of empirical evidence, rather than a systematic analysis stratified by resolution or geometric complexity. Even so, this is a relatively new setting, and strictly comparable, reproducible baselines for full spatio-temporal EP prediction on 3D biventricular meshes are limited. The main contribution of the paper is the combination of an anatomy-aware GNN with explicit electrophysiology physics constraints for spatio-temporal EP prediction on realistic biventricular meshes. Overall, the rebuttal suggests that several of the original concerns were due to missing experimental details and unclear presentation, rather than fundamental flaws in the method.
Author Feedback
We thank the reviewers for the encouraging comments, including “leading to more physically plausible predictions compared to purely data-driven baselines” (R1), “well aligned with the requirements of cardiac digital twins” (R2), and “more in line with the mechanism structure of cardiac EP” (R3). Our responses to the major concerns are as follows. 1.Clinical applicability (R1.1) We agree that validation on clinical EP propagation is an important future direction. However, dense spatiotemporal EP ground truth remains difficult to obtain due to the invasive nature of clinical mapping systems; therefore, simulation-based supervision remains common in cardiac EP learning studies (JETP Letters, 2025). Although the Aliev-Panfilov model is simplified compared to detailed ionic formulations, it remains widely used for propagation and reentrant dynamics studies due to its favorable balance between physiological fidelity and computational efficiency (PLoS One, 2020). Moreover, the proposed framework is not restricted to Aliev-Panfilov and can be extended to more complex ionic models by simply adjusting the decoder outputs and corresponding reaction ODE losses. 2.Mesh details & computational efficiency (R1.3,R2.2,R3.4) Training used meshes with ~40–60k hexahedral elements, while testing used higher-resolution anatomies (~300–500k elements). All experiments were performed on a single NVIDIA A40 GPU. The model was trained for 100 epochs (~0.5h/epoch), while the data-driven baseline was obtained by setting λ_ode=λ_pde=0 in Eq.(7). Inference required 0.128s/frame, compared to ~2.15s/frame for the FEM solver (MonoAlg3D), supporting the computational efficiency claim. 3.Clarification of variables (R2.1,R3.3) I_stim denotes the external stimulation current, applied only at the initial frame; thus, I_stim = 0 in the subsequent physics-informed loss. We denote I as the set of interior cardiac cells (graph nodes). In the Aliev-Panfilov model, u is the normalized transmembrane potential Vm, computed as u = (Vm + Vmin)/(Vmax + Vmin), where Vmin and Vmax are the minimum and maximum voltage values in the dataset. Sv corresponds to the state variable z in Eq.(7). 4.Baseline fairness (R1.2,R3.1) This study addresses a relatively novel setting: predicting full spatiotemporal action potential dynamics directly from 3D bi-ventricular anatomies. Consequently, comparable EP surrogate baselines remain limited. Specifically, [10,13,16] only evaluated simplified 2D settings, [14] requires LAT maps as additional inputs, and [17] predicts only activation-time maps instead of full temporal voltage dynamics. In addition, many prior works do not provide public code or reproducible pipelines. Therefore, we primarily compared against the pure data-driven counterpart to isolate the contribution of physics-informed training. AGATA [18] was included as the closest related framework; however, due to unavailable code, we only reported the activation-time MAE from the original paper for reference. 5.Cross-resolution generalization & choice of time horizon (R2.3,R3.2) Due to the local message-passing mechanism of GNNs, the model learns local propagation dynamics from neighboring cells rather than global waveforms, making it less sensitive to resolution changes. Long training horizons are also unnecessary and computationally expensive, since the transmembrane potential and state variables are mainly updated from the immediately preceding step according to Eq.(3),(4). T=4 was introduced to improve robustness against accumulated autoregressive errors. In our previous experiments, for 40 ms future prediction, T=2 achieved PCC=0.62 with 7246 MB peak GPU memory usage, T=4 achieved the best PCC=0.75 with 12326 MB, while T=6 slightly decreased performance (PCC =0.68) and increased memory usage to 27135 MB. Therefore, T=4 was selected as the best balance between accuracy and computational cost and was not explained in detail due to the space constraint.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
This paper received mixed scores 3, 4, 4.Concerns include the presentation clarity and experimental evaluations. AC invites the authors for a rebuttal to clear the concerns raised by all reviewers.
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
The rebuttal addressed major concerns raised by reviewers, and all reviewers agree on its acceptance. It is a clear accept.
Meta-review #2
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
The reviewers recognize the clinical relevance of the problem, the technically sound physics-informed GNN design, and the meaningful generalization across unseen biventricular geometries. Concerns about missing experimental details, baseline fairness, and notation inconsistencies were largely addressed in the rebuttal.
All three reviewers updated their recommendation to accept after the rebuttal. The paper is therefore recommended for acceptance.
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
The authors have done a good job to address many of the reviews concerns during the rebuttal phase. But please be more careful with the strength of the claims you make.